convex relaxations of 0 1 quadratic programming we consider three parametric relaxations of the 0 l quadratic programming problem these relaxations are to quadratic maximization over simple box constraints quadratic maximization over the sphere and the maximum eigenvalue of a bordered matrix when minimized over the parameter each of the relaxations provides an upper bound on the original discrete problem moreover these bounds are efficiently computable our main result is that surprisingly all three bounds are equal

on the bridge between combinatorial optimization and nonlinear optimization a family of semidefinite bounds for 0 1 quadratic problems leading to quasi newton methods this article presents a family of semidefinite programming bounds obtained by lagrangian duality for 0 1 quadratic optimization problems with linear or quadratic constraints these bounds have useful computational properties they have a good ratio of tightness to computing time they can be optimized by a quasi newton method and their final tightness level is controlled by a real parameter these properties are illustrated on three standard combinatorial optimization problems unconstrained 0 1 quadratic optimization heaviest k subgraph and graph bisection

detection of signals by information theoretic criteria a new approach is presented to the problem of detecting the number of signals in a multichannel time series based on the application of the information theoretic criteria for model selection introduced by akaike aic and by schwartz and rissanen mdl unlike the conventional hypothesis testing based approach the new approach does not requite any subjective threshold settings the number of signals is obtained merely by minimizing the aic or the mdl criteria simulation results that illustrate the performance of the new method for the detection of the number of signals received by a sensor array are presented

extending the qcr method to general mixed integer programs let mqp be a general mixed integer quadratic program that consists of minimizing a quadratic function subject to linear constraints in this paper we present a convex reformulation of mqp i e we reformulate mqp into an equivalent program with a convex objective function such a reformulation can be solved by a standard solver that uses a branch and bound algorithm we prove that our reformulation is the best one within a convex reformulation scheme from the continuous relaxation point of view this reformulation that we call miqcr mixed integer quadratic convex reformulation is based on the solution of an sdp relaxation of mqp computational experiences are carried out with instances of mqp including one equality constraint or one inequality constraint the results show that most of the considered instances with up to 40 variables can be solved in 1 h of cpu time by a standard solver

novel partitioned time integration methods for dae systems based on l stable linearly implicit algorithms real time applications based on the principle of dynamic substructuring require integration methods that can deal with constraints without exceeding an a priori fixed number of steps for these applications first we introduce novel partitioned algorithms able to solve daes arising from transient structural dynamics in particular the spatial domain is partitioned into a set of disconnected subdomains and continuity conditions of acceleration at the interface are modeled using a dual schur formulation interface equations along with subdomain equations lead to a system of daes for which both staggered and parallel procedures are developed moreover under the framework of projection methods also a parallel partitioned method is conceived the proposed partitioned algorithms enable a rosenbrock based linearly implicit lsrt2 method to be strongly coupled with different time steps in each subdomain thus user defined algorithmic damping and subcycling strategies are allowed secondly the paper presents the convergence analysis of the novel schemes for linear single degree of freedom dof systems the algorithms are generally a stable and preserve the accuracy order as the original monolithic method successively these results are validated via simulations on single and three dofs systems finally the insight gained from previous analyses is confirmed by means of numerical experiments on a coupled spring pendulum system copyright 2011 john wiley sons ltd

computational experience with a bundle approach for semidefinite cutting plane relaxations of max cut and equipartition we propose a dynamic version of the bundle method to get approximate solutions to semidefinite programs with a nearly arbitrary number of linear inequalities our approach is based on lagrangian duality where the inequalities are dualized and only a basic set of constraints is maintained explicitly this leads to function evaluations requiring to solve a relatively simple semidefinite program our approach provides accurate solutions to semidefinite relaxations of the max cut and the equipartition problem which are not achievable by direct approaches based only on interior point methods

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

estimating the number of sinusoids in additive white noise the test proposed uses the eigenvector decomposition of the estimated autocorrelation matrix and is based on matrix perturbation analysis the estimator is shown to be able to resolve closely spaced sinusoids at lower signal to noise ratios than heuristic tests simulation results for two closely spaced sinusoids are detailed several unanswered questions are discussed

on the minimization of total weighted flow time with identical and uniform parallel machines we consider the np hard problem of scheduling jobs on identical parallel machines to minimize total weighted flow time we discuss the properties that characterize the structure of an optimal solution present a lower bound and propose a branch and bound algorithm the algorithm is superior to prior methods presented in the literature we also extend the algorithm to uniform parallel machines and solve medium sized problem instances

a semi supervised random vector functional link network based on the transductive framework semi supervised learning ssl is the problem of learning a function with only a partially labeled training set it has considerable practical interest in applications where labeled data is costly to obtain while unlabeled data is abundant one approach to ssl in the case of binary classification is inspired by work on transductive learning tl by vapnik it has been applied prevalently using support vector machines svm as the base learning algorithm giving rise to the so called transductive svm tr svm the resulting optimization problem however is highly non convex and complex to solve in this paper we propose an alternative semi supervised training algorithm based on the tl theory namely semi supervised random vector functional link rvfl network which is able to obtain state of the art performance while resulting in a standard convex optimization problem in particular we show that thanks to the characteristics of rvfls networks the resulting optimization problem can be safely approximated with a standard quadratic programming problem solvable in polynomial time a wide range of experiments validate our proposal as a comparison we also propose a semi supervised algorithm for rvfls based on the theory of manifold regularization

branch and price column generation for solving huge integer programs we discuss formulations of integer programs with a huge number of variables and their solution by column generation methods i e implicit pricing of nonbasic variables to generate new columns or to prove lp optimality at a node of the branch and bound tree we present classes of models for which this approach decomposes the problem provides tighter lp relaxations and eliminates symmetry we then discuss computational issues and implementation of column generation branch and bound algorithms including special branching rules and efficient ways to solve the lp relaxation we also discuss the relationship with lagrangian duality

identification of parametric underspread linear systems and super resolution radar identification of time varying linear systems which introduce both time shifts delays and frequency shifts doppler shifts is a central task in many engineering applications this paper studies the problem of identification of underspread linear systems ulss whose responses lie within a unit area region in the delay doppler space by probing them with a known input signal it is shown that sufficiently underspread parametric linear systems described by a finite set of delays and doppler shifts are identifiable from a single observation as long as the time bandwidth product of the input signal is proportional to the square of the total number of delay doppler pairs in the system in addition an algorithm is developed that enables identification of parametric ulss from an input train of pulses in polynomial time by exploiting recent results on sub nyquist sampling for time delay estimation and classical results on recovery of frequencies from a sum of complex exponentials finally application of these results to super resolution target detection using radar is discussed specifically it is shown that the proposed procedure allows to distinguish between multiple targets with very close proximity in the delay doppler space resulting in a resolution that substantially exceeds that of standard matched filtering based techniques without introducing leakage effects inherent in recently proposed compressed sensing based radar methods

a numerical scheme to couple subdomains with different time steps for predominantly linear transient analysis abstract this paper generalizes the explicit implicit time integration algorithms pioneered by belytschko hughes and their respective co workers and the feti domain decomposition methods introduced by farhat and his co workers to the case where the same newmark scheme but different and coefficients and different time steps are specified in each subdomain building upon the work of farhat crivelli and geradin it considers various interface boundary constraints and performs a stability analysis of the proposed time integration algorithms

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

zur effektiven losung von booleschen quadratischen optimierungsproblemen the dual of the boolean quadratic programming problem is considered the optimal value of their objective function gives bounds for the branch and bound process which seem to be better then known from other autors es wird die zum booleschen quadratischen optimierungsproblem duale aufgabe untersucht ihr optimaler zielfunktionswert liefert wesentlich scharfere schranken fur den branch and bound proze als die bisher verwendeten

subspace based estimation of time delays and doppler shifts this paper considers the problem of estimating the time delays and doppler shifts of a known waveform received via several distinct paths by an array of antennas the general maximum likelihood estimator is presented and is shown to require a 2d dimensional nonlinear minimization where d is the number of received signal reflections two alternative solutions based on signal and noise subspace fitting are proposed requiring only a d dimensional minimization in particular we show how to decouple the required search into a two step procedure where the delays are estimated and the dopplers solved for explicitly initial conditions for the time delay search can be obtained by applying generalizations of the music and esprit algorithms which are also outlined in the paper simulation examples are included to illustrate the algorithms performance relative to the cramer rao bound

using a mixed integer quadratic programming solver for the unconstrained quadratic 0 1 problem in this paper we consider problem p of minimizing a quadratic function q x x tqx ctx of binary variables our main idea is to use the recent mixed integer quadratic programming miqp solvers but for this we have to first convexify the objective function q x a classical trick is to raise up the diagonal entries of q by a vector u until q diag u is positive semidefinite then using the fact that xi2 xi we can obtain an equivalent convex objective function which can then be handled by an miqp solver hence computing a suitable vector u constitutes a preprocessing phase in this exact solution method we devise two different preprocessing methods the first one is straightforward and consists in computing the smallest eigenvalue of q in the second method vector u is obtained once a classical sdp relaxation of p is solved we carry out computational tests using the generator of pardalos and rodgers 1990 and we compare our two solution methods to several other exact solution methods furthermore we report computational results for the max cut problem

worst case bound of an lrf schedule for the mean weighted flow time problem this paper studies the problem of scheduling a set of n independent tasks on m identical processors so as to minimize mean weighted flow time the problem is known to be np complete for m geqq 2 and to be np complete in the strong sense for m arbitrary the worst case behavior of a heuristic algorithm which requires time o n log n is investigated and it is shown that the mean weighted flow time obtained by the algorithm does not exceed sqrt 2 1 2 cong 1 0207 times that of an optimal schedule moreover the bound sqrt 2 1 2 is best possible

arlequin framework for multi model multi time scale and heterogeneous time integrators for structural transient dynamics this paper presents a general framework for performing spatio temporal multi scale multi model coupling based on displacement continuity this approach guarantees a global energy balance of the system in the context of the arlequin method it introduces specific interpolation of the lagrange multipliers and parameters of time integration operators in the overlapping zone a dual schur implementation is then used to illustrate the efficiency and robustness of the method convergence analysis with numerical experiments is performed finally 1d 1d and 2d 1d coupling applications are presented in which each subdomain is integrated in time using different time steps and different schemes this approach gives the user more ways of controlling computational behaviour via newmark parameters time steps and sizing the overlapping zones

a new optimization algorithm for the vehicle routing problem with time windows the vehicle routing problem with time windows vrptw is a generalization of the vehicle routing problem where the service of a customer can begin within the time window defined by the earliest and the latest times when the customer will permit the start of service in this paper we present the development of a new optimization algorithm for its solution the lp relaxation of the set partitioning formulation of the vrptw is solved by column generation feasible columns are added as needed by solving a shortest path problem with time windows and capacity constraints using dynamic programming the lp solution obtained generally provides an excellent lower bound that is used in a branch and bound algorithm to solve the integer set partitioning formulation our results indicate that this algorithm proved to be successful on a variety of practical sized benchmark vrptw test problems the algorithm was capable of optimally solving 100 customer problems this problem size is six times larger than any reported to date by other published research

a comparison of branch and bound algorithms for a family scheduling problem with identical parallel machines this paper investigates branch and bound algorithms for the problem of scheduling jobs with family setups on identical parallel machines to minimize the weighted sum of completion times in particular we propose a new branching scheme that appears to substantially outperform current procedures in terms of computation time and search tree size

roof duality complementation and persistency in quadratic 0 1 optimization the paper is concerned with the primal problem of maximizing a given quadratic pseudo boolean function four equivalent problems are discussed the primal the complementation the discrete rhys lp and the weighted stability problem of a sam graph each of them has a relaxation the roof dual the quadratic complementation the continuous rhys lp and the fractional weighted stability problem of a sam graph the main result is that the four gaps associated with the four relaxations are equal furthermore a solution to any of these problems leads at once to solutions of the other three equivalent ones the four relaxations can be solved in polynomial time by transforming them to a bipartite maximum flow problem the optimal solutions of the roof dual define best linear majorantsp x off having the following persistency property if theith coefficient inp is positive negative thenx i 1 0 in every optimum of the primal problem several characterizations are given for the case where these persistency results cannot be used to fix any variable of the primal on the other hand a class of gap free functions properly including the supermodular ones is exhibited

cramer rao lower bounds for the joint delay doppler estimation of an extended target the problem of the cramer rao lower bounds crlbs for the joint time delay and doppler stretch estimation of an extended target is considered in this paper integral representations of the crlbs for both the time delay and the doppler stretch are derived to facilitate computation and analysis series representations and approximations of the crlbs are introduced according to these series representations the impact of several waveform parameters on the estimation accuracy is investigated and reveals that the crlb of the doppler stretch is inversely proportional to the effective time bandwidth product of the waveform this conclusion generalizes a previous result in the narrowband case the popular wideband ambiguity function wbaf based delay doppler estimator is evaluated and compared with the crlbs through numerical experiments our results indicate that the wbaf estimator which was originally derived from a single scatterer model is not suitable for the parameter estimation of an extended target

a feti based multi time step coupling method for newmark schemes in structural dynamics we present an efficient and accurate multi time step coupling method using feti domain decomposition for structural dynamics using this method one can divide a large structural mesh into a number of smaller subdomains solve the individual subdomains separately and couple the solutions together to obtain the solution to the original problem the various subdomains can be integrated in time using different time steps and or different newmark schemes this approach will be most effective for very large scale simulations on complex geometries our coupling method builds upon a method previously proposed by gravouil and combescure gc method we show that for the simplest case when the same time step is used in all subdomains of the mesh our method reduces to the gc method and is unconditionally stable and energy preserving in addition we show that our method possesses these desirable properties for general multi time step cases too unlike the gc method which is dissipative greater computational efficiency is also achieved through our method by limiting the computation of interface forces to the largest time step as opposed to the smallest time step in the gc method copyright 2004 john wiley sons ltd

duality gap estimation of linear equality constrained binary quadratic programming we investigate in this paper the lagrangian duality properties of linear equality constrained binary quadratic programming we derive an underestimation of the duality gap between the primal problem and its lagrangian dual or sdp relaxation using the distance from the set of binary integer points to certain affine subspace while the computation of this distance can be achieved by the cell enumeration of hyperplane arrangement alternative lagrangian dual schemes via the exact penalty and the squared norm constraint reformulations are also discussed

esprit estimation of signal parameters via rotational invariance techniques an approach to the general problem of signal parameter estimation is described the algorithm differs from its predecessor in that a total least squares rather than a standard least squares criterion is used although discussed in the context of direction of arrival estimation esprit can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise it exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure the technique when applicable manifests significant performance and computational advantages over previous algorithms such as mem capon s mlm and music

solving max cut to optimality by intersecting semidefinite and polyhedral relaxations we present a method for finding exact solutions of max cut the problem of finding a cut of maximum weight in a weighted graph we use a branch and bound setting that applies a dynamic version of the bundle method as bounding procedure this approach uses lagrangian duality to obtain a nearly optimal solution of the basic semidefinite max cut relaxation strengthened by triangle inequalities the expensive part of our bounding procedure is solving the basic semidefinite relaxation of the max cut problem which has to be done several times during the bounding process we review other solution approaches and compare the numerical results with our method we also extend our experiments to instances of unconstrained quadratic 0 1 optimization and to instances of the graph equipartition problem the experiments show that our method nearly always outperforms all other approaches in particular for dense graphs where linear programming based methods fail our method performs very well exact solutions are obtained in a reasonable time for any instance of size up to n 100 independent of the density for some problems of special structure we can solve even larger problem classes we could prove optimality for several problems of the literature where to the best of our knowledge no other method is able to do so

solving quadratic 0 1 problems by semidefinite programs and cutting planes we present computational experiments for solving quadratic 0 1 problems our approach combines a semidefinite relaxation with a cutting plane technique and is applied in a branch and bound setting our experiments indicate that this type of approach is very robust and allows to solve many moderately sized problems having say less than 100 binary variables in a routine manner 1998 the mathematical programming society inc published by elsevier science b v

on the cramer rao bound for time delay and doppler estimation corresp using a theorem due to whittle simple derivations of the cramer rao lower bound are presented for some delay estimation problems related to a single source multiple sources and multipath the problem of doppler estimation is briefly discussed

lower bounds for the earliness tardiness scheduling problem on parallel machines with distinct due dates this paper addresses the parallel machine scheduling problem in which the jobs have distinct due dates with earliness and tardiness costs new lower bounds are proposed for the problem they can be classed into two families first two assignment based lower bounds for the one machine problem are generalized for the parallel machine case second a time indexed formulation of the problem is investigated in order to derive efficient lower bounds throught column generation or lagrangean relaxation a simple local search algorithm is also presented in order to derive an upper bound computational experiments compare these bounds for both the one machine and parallel machine problems and show that the gap between upper and lower bounds is about 1 5

convex quadratic and semidefinite programming relaxations in scheduling we consider the problem of scheduling unrelated parallel machines subject to release dates so as to minimize the total weighted completion time of jobs the main contribution of this paper is a provably good convex quadratic programming relaxation of strongly polynomial size for this problem the best previously known approximation algorithms are based on lp relaxations in time or interval indexed variables those lp relaxations however suffer from a huge number of variables as a result of the convex quadratic programming approach we can give a very simple and easy to analyze 2 approximation algorithm which can be further improved to performance guarantee 3 2 in the absence of release dates we also consider preemptive scheduling problems and derive approximation algorithms and results on the power of preemption which improve upon the best previously known results for these settings finally for the special case of two machines we introduce a more sophisticated semidefinite programming relaxation and apply the random hyperplane technique introduced by goemans and williamson for the maxcut problem this leads to an improved 1 2752 approximation

a spectral bundle method for semidefinite programming a central drawback of primal dual interior point methods for semidefinite programs is their lack of ability to exploit problem structure in cost and coefficient matrices this restricts applicability to problems of small dimension typically semidefinite relaxations arising in combinatorial applications have sparse and well structured cost and coefficient matrices of huge order we present a method that allows us to compute acceptable approximations to the optimal solution of large problems within reasonable time semidefinite programming problems with constant trace on the primal feasible set are equivalent to eigenvalue optimization problems these are convex nonsmooth programming problems and can be solved by bundle methods we propose replacing the traditional polyhedral cutting plane model constructed from subgradient information by a semidefinite model that is tailored to eigenvalue problems convergence follows from the traditional approach but a proof is included for completeness we present numerical examples demonstrating the efficiency of the approach on combinatorial examples

estimating the parameters of exponentially damped sinusoids and pole zero modeling in noise we have presented techniques 1 6 based on linear prediction lp and singular value decomposition svd for accurate estimation of closely spaced frequencies of sinusoidal signals in noise in this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise the estimation procedure presented here makes use of backward prediction in addition to svd first the method is applied to data consisting of one and two exponentially damped sinusoids the choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate cramer rao cr bounds and to traditional methods of linear prediction second our method is applied to an example due to steiglitz 8 in which the data consists of noisy values of the impulse response samples composed of many exponentially damped sinusoids of a linear system having both poles and zeros the poles of the system are accurately determined by our method and the zeros are obtained subsequently using shanks method

column generation algorithms for exact modularity maximization in networks finding modules or clusters in networks currently attracts much attention in several domains the most studied criterion for doing so due to newman and girvan phys rev e 69 026113 2004 is modularity maximization many heuristics have been proposed for maximizing modularity and yield rapidly near optimal solution or sometimes optimal ones but without a guarantee of optimality there are few exact algorithms prominent among which is a paper by xu et al eur phys j b 60 231 2007 modularity maximization can also be expressed as a clique partitioning problem and the row generation algorithm of grotschel and wakabayashi math program 45 59 1989 applied we propose to extend both of these algorithms using the powerful column generation methods for linear and non linear integer programming performance of the four resulting algorithms is compared on problems from the literature instances with up to 512 entities are solved exactly moreover the computing time of previously solved problems are reduced substantially

robust matched filtering in ell_ p space a common approach to time delay estimation tde and joint delay doppler estimation jdde for target localization is matched filtering which is equivalent to the cross correlation of the received and transmitted signals the conventional correlation in hilbert space is statistically optimal in white gaussian noise however its performance significantly degrades in the presence of non gaussian noise or clutter in this paper two new concepts called ell p correlation and ell p ambiguity functions which generalize the conventional matched filtering from hilbert space to ell p space are proposed in addition several important mathematical properties of the ell p correlation and ell p ambiguity functions are given and proved compared with conventional ambiguity function the time frequency concentration of the ell p ambiguity function is significantly enhanced i e the delay doppler resolution is improved and the sidelobes are suppressed based on these two newly defined functions a family of tde and jdde algorithms that are robust against impulsive noise or clutter are developed furthermore the cramer rao bounds of tde and jdde for non gaussian noise with arbitrary probability distribution are derived simulation results under several impulsive noise models demonstrate that the performance in terms of robustness resolution and estimation accuracy is substantially improved when compared with the conventional matched filtering and fractional lower order moment based methods

adaptive memory tabu search for binary quadratic programs recent studies have demonstrated the effectiveness of applying adaptive memory tabu search procedures to combinatorial optimization problems in this paper we describe the development and use of such an approach to solve binary quadratic programs computational experience is reported showing that the approach optimally solves the most difficult problems reported in the literature for challenging problems of limited size which are capable of being approached by exact procedures we find optimal solutions considerably faster than the best reported exact method moreover we demonstrate that our approach is significantly more efficient and yields better solutions than the best heuristic method reported to date finally we give outcomes for larger problems that are considerably more challenging than any currently reported in the literature

a feasible active set method for strictly convex quadratic problems with simple bounds a primal dual active set method for quadratic problems with bound constraints is presented which extends the infeasible active set approach of kunisch and rendl siam j optim 14 2003 pp 35 52 based on a guess of the active set a primal dual pair x alpha is computed that satisfies stationarity and the complementary condition if x is not feasible the variables connected to the infeasibilities are added to the active set and a new primal dual pair x alpha is computed this process is iterated until a primal feasible solution is generated then a new active set is determined based on the feasibility information of the dual variable alpha strict convexity of the quadratic problem is sufficient for the algorithm to stop after a finite number of steps with an optimal solution computational experience indicates that this approach also performs well in practice

spectral bounds for unconstrained 1 1 quadratic optimization problems abstract given an unconstrained quadratic optimization problem in the following form qp min x t qx x 1 1 n with q r n n we present different methods for computing bounds on its optimal objective value some of the lower bounds introduced are shown to generally improve over the one given by a classical semidefinite relaxation we report on theoretical results on these new bounds and provide preliminary computational experiments on small instances of the maximum cut problem illustrating their performance

logical and inequality implications for reducing the size and difficulty of quadratic unconstrained binary optimization problems abstract the quadratic unconstrained binary optimization qubo problem arises in diverse optimization applications ranging from ising spin problems to classical problems in graph theory and binary discrete optimization the use of preprocessing to transform the graph representing the qubo problem into a smaller equivalent graph is important for improving solution quality and time for both exact and metaheuristic algorithms and is a step towards mapping large scale qubo to hardware graphs used in quantum annealing computers in an earlier paper a set of rules was introduced that achieved significant qubo reductions as verified through computational testing here this work is extended with additional rules that provide further reductions that succeed in exactly solving 10 of the benchmark qubo problems an algorithm and associated data structures to efficiently implement the entire set of rules is detailed and computational experiments are reported that demonstrate their efficacy

earliness tardiness scheduling problems i weighted deviation of completion times about a common due date this paper and its companion part ii concern the scheduling of jobs with cost penalties for both early and late completion in part i we consider the problem of minimizing the weighted sum of earliness and tardiness of jobs scheduled on a single processor around a common due date d we assume that d is not early enough to constrain the scheduling decision the weight of a job does not depend on whether the job is early or late but weights may vary between jobs we prove that the recognition version of this problem is np complete in the ordinary sense we describe optimality conditions and present a computationally efficient dynamic programming algorithm when the weights are bounded by a polynomial function of the number of jobs a fully polynomial approximation scheme is given we also describe four special cases for which the problem is polynomially solvable part ii provides similar results for the unweighted version of this problem where d is arbitrary

a column generation approach for the unconstrained binary quadratic programming problem abstract this paper proposes a column generation approach based on the lagrangean relaxation with clusters to solve the unconstrained binary quadratic programming problem that consists of maximizing a quadratic objective function by the choice of suitable values for binary decision variables the proposed method treats a mixed binary linear model for the quadratic problem with constraints represented by a graph this graph is partitioned in clusters of vertices forming sub problems whose solutions use the dual variables obtained by a coordinator problem the column generation process presents alternative ways to find upper and lower bounds for the quadratic problem computational experiments were performed using hard instances and the proposed method was compared against other methods presenting improved results for most of these instances

improved semidefinite bounding procedure for solving max cut problems to optimality we present an improved algorithm for finding exact solutions to max cut and the related binary quadratic programming problem both classic problems of combinatorial optimization the algorithm uses a branch and cut and bound paradigm using standard valid inequalities and nonstandard semidefinite bounds more specifically we add a quadratic regularization term to the strengthened semidefinite relaxation in order to use a quasi newton method to compute the bounds the ratio of the tightness of the bounds to the time required to compute them can be controlled by two real parameters we show how adjusting these parameters and the set of strengthening inequalities gives us a very efficient bounding procedure embedding our bounding procedure in a generic branch and bound platform we get a competitive algorithm extensive experiments show that our algorithm dominates the best existing method

a branch and price algorithm for scheduling parallel machines with sequence dependent setup times abstract we consider the problem of scheduling n independent jobs on m unrelated parallel machines with sequence dependent setup times and availability dates for the machines and release dates for the jobs to minimize a regular additive cost function in this work we develop a new branch and price optimization algorithm for the solution of this general class of parallel machines scheduling problems a new column generation accelerating method termed primal box and a specific branching variable selection rule that significantly reduces the number of explored nodes are proposed the computational results show that the approach solves problems of large size to optimality within reasonable computational time

on multi time step monolithic coupling algorithms for elastodynamics we present a way of constructing multi time step monolithic coupling methods for elastodynamics the governing equations for constrained multiple subdomains are written in dual schur form and the continuity of velocities is enforced at system time levels the resulting equations will be in the form of differential algebraic equations to crystallize the ideas we shall employ newmark family of time stepping schemes the proposed method can handle multiple subdomains and allows different time steps as well as different time stepping schemes from the newmark family in different subdomains we shall use the energy method to assess the numerical stability and quantify the influence of perturbations under the proposed coupling method two different notions of energy preservation are introduced and employed to assess the performance of the proposed method several numerical examples are presented to illustrate the accuracy and stability properties of the proposed method we shall also compare the proposed multi time step coupling method with some other methods available in the literature

brief paper convex relaxations for mixed integer predictive control the main objective in this work is to compare different convex relaxations for model predictive control mpc problems with mixed real valued and binary valued control signals in the problem description considered the objective function is quadratic the dynamics are linear and the inequality constraints on states and control signals are all linear the relaxations are related theoretically and the quality of the bounds and the computational complexities are compared in numerical experiments the investigated relaxations include the quadratic programming qp relaxation the standard semidefinite programming sdp relaxation and an equality constrained sdp relaxation the equality constrained sdp relaxation appears to be new in the context of hybrid mpc and the result presented in this work indicates that it can be useful as an alternative relaxation which is less computationally demanding than the ordinary sdp relaxation and which often gives a better bound than the bound from the qp relaxation furthermore it is discussed how the result from the sdp relaxations can be used to generate suboptimal solutions to the control problem moreover it is also shown that the equality constrained sdp relaxation is equivalent to a qp in an important special case

maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements the problem of estimating the frequencies phases and amplitudes of sinusoidal signals is considered a simplified maximum likelihood gauss newton algorithm which provides asymptotically efficient estimates of these parameters is proposed initial estimates for this algorithm are obtained by a variation of the overdetermined yule walker method and periodogram based procedure use of the maximum likelihood gauss newton algorithm is not however limited to this particular initialization method some other possibilities to get suitable initial estimates are briefly discussed an analytical and numerical study of the shape of the likelihood function associated with the sinusoids in noise process reveals its multimodal structure and clearly sets the importance of the initialization procedure some numerical examples are presented to illustrate the performance of the proposed estimation procedure comparison to the performance corresponding to the cramer rao lower bound is also presented using a simple expression for the asymptotic cramer rao bound covariance matrix derived in the paper

a new partitioned staggered scheme for flexible multibody interactions with strong inertial effects abstract in generic flexible multibody interaction problems the differences in the mass damping and stiffness of the bodies can be very large of particular interest is a small change in the higher mass structure which triggers relatively large inertial effects on the lower mass structure in this work a new partitioned staggered time integration scheme is developed and its applicability is extended to the problems involving low mass ratios in coupled multibody problems the equation of motion of body with larger inertia is integrated by implicit newmark method whereas the smaller inertia is solved using a robust self starting explicit integration procedure the coupled formulation includes explicit correction terms that adjusts the amount of interfacial velocity which plays a key role in the stability and accuracy of the simulations a wide range of mass 10 6 10 1 damping and stiffness 10 3 10 3 ratios are chosen to assess the stability and accuracy characteristics of the proposed scheme the closed form expressions for the coupling parameter have been constructed for both matching and non matching time stepping through the godunov ryabenkii normal mode analysis the stability of the proposed method is observed as a function of the relative properties and temporal discretisation of the coupled system the time step of the heavier body significantly influences the stability more than the lighter body to maintain the staggering error minimal an optimal range of the coupling parameter is identified the error computed with uniform variation in the time step revealed that the present method is more accurate than the existing methods the partitioned method is an energy preserving integration method for the dynamic analysis of multibody systems as a potential application of this scheme flexible multibody problems in the field of offshore engineering viz wave energy converter and floater mooring systems are presented and validated with experimental measurements

optimal solutions for unrelated parallel machines scheduling problems using convex quadratic reformulations abstract in this work we take advantage of the powerful quadratic programming theory to obtain optimal solutions of scheduling problems we apply a methodology that starts in contrast to more classical approaches by formulating three unrelated parallel machine scheduling problems as 0 1 quadratic programs under linear constraints by construction these quadratic programs are non convex therefore before submitting them to a branch and bound procedure we reformulate them in such a way that we can ensure convexity and a high quality continuous lower bound experimental results show that this methodology is interesting by obtaining the best results in literature for two of the three studied scheduling problems

an interior point method for semidefinite programming we propose a new interior point based method to minimize a linear function of a matrix variable subject to linear equality and inequality constraints over the set of positive semidefinite matrices

two feti based heterogeneous time step coupling methods for newmark and α schemes derived from the energy method abstract the purpose of this paper is to describe a general methodology to obtain multi time step coupling methods for different time integration schemes newmark hht wbz ch on the basis of energetic considerations the general framework of the feti method is considered for building the heterogeneous time step coupling methods by ensuring the gluing of subdomains with lagrange multipliers the proposed methods for coupling subdomains with different time integration schemes and time steps fine and large time steps are based on the pseudo energy measure as introduced by hughes in the so called energy method employed for proving the stability of implicit explicit algorithms assuming a given variation of the lagrange multipliers over the large time step kinematic conditions are derived by ensuring the zero pseudo energy at the interface two methods will be derived in this paper the first new method for which the interface problem involving the lagrange multipliers is solved at the large time scale can handle the popular dissipative schemes hht wbz ch in the particular case of the newmark schemes the new method matches with the ph method proposed by prakash and hjelmstad the second new method is based at the micro time scale it can be viewed as an extension of the method proposed by gravouil and combescure gc method for the coupling of the schemes nonetheless like the gc method the new micro time based method turns out to be dissipative when non dissipative second order accurate schemes are involved and looses one order of accuracy

multi time step explicit implicit method for non linear structural dynamics we present a method with domain decomposition to solve time dependent non linear problems this method enables arbitrary numeric schemes of the newmark family to be coupled with different time steps in each subdomain this coupling is achieved by prescribing continuity of velocities at the interface we are more specifically interested in the coupling of implicit explicit numeric schemes taking into account material and geometric non linearities the interfaces are modelled using a dual schur formulation where the lagrange multipliers represent the interfacial forces unlike the continuous formulation the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements velocities and accelerations at the interfaces we show that within the framework of the newmark family of numeric schemes continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged to prove this stability we use an energy method i e a global method over the whole time interval in order to verify the algorithms properties then we propose to extend this to non linear situations in the following cases implicit linear explicit non linear explicit non linear explicit non linear and implicit non linear explicit non linear finally we present some examples showing the feasibility of the method copyright 2001 john wiley sons ltd

a new approach for crew pairing problems by column generation with an application to air transportation we propose a new approach to crew pairing problems arising in the context of airline companies the problem is first formulated as a large scale set covering problem with many colums each column representing a valid crew pairing we then suggest a solution procedure for the continuous relaxation of this large scale problem based on generalized linear programming in which the column generation subproblem is shown to be equivalent to a shortest path problem in an associated graph computational results obtained on a series of real problems involving up to 329 flight segments are reported confirming both computational efficiency and practical applicability of the new approach indeed not only were the resulting solutions observed to be integral for most test problems but average savings of about 4 to 5 over the best available hand built solutions were shown to be obtained

measurement of time variant linear channels the goal of channel measurement or operator identification is to obtain complete knowledge of a channel operator by observing the image of a finite number of input signals in this paper it is shown that the spreading support of the operator that is the support of the symplectic fourier transform of the kohn nirenberg symbol of the operator has area less than one then the operator is identifiable if the spreading support is larger than one then the operator is not identifiable the shape of the support region is essentially arbitrary thereby proving a conjecture of bello the input signal considered is a weighted delta train where the weights are the window function of a finite gabor system whose elements satisfy a certain robust completeness property

an efficient parametric technique for doppler delay estimation receiving an output signal that is a weighted sum of doppler and delay shifted versions of an input signal arises in various engineering systems including radar sonar and communications it is often desired to estimate the doppler and delay parameters from noisy measurements of the output signal an estimation algorithm is developed herein for the doppler frequencies delays and amplitudes for a specific choice of the input the algorithm is based on a computationally efficient search free frequency estimation technique for the sum of complex exponentials asymptotic performance bounds are developed for the estimated parameters simulation results show that the variance of the estimation error is close to the bound above a threshold signal to noise ratio indicating that the estimation algorithm is statistically efficient

a scalable lagrange multiplier based domain decomposition method for time dependent problems we present a new efficient and scalable domain decomposition method for solving implicitly linear and non linear time dependent problems in computational mechanics the method is derived by adding a coarse problem to the recently proposed transient feti substructuring algorithm in order to propagate the error globally and accelerate convergence it is proved that in the limit for large time steps the new method converges toward the feti algorithm for time independent problems computational results confirm that the optimal convergence properties of the time independent feti method are preserved in the time dependent case we employ an iterative scheme for solving efficiently the coarse problem on massively parallel processors and demonstrate the effective scalability of the new transient feti method with the large scale finite element dynamic analysis on the paragon xp s and ibm sp2 systems of several diffraction grating finite element structural models we also show that this new domain decomposition method outperforms the popular direct skyline solver the coarse problem presented herein is applicable and beneficial to a large class of lagrange multiplier based substructuring algorithms for time dependent problems including the fictitious domain decomposition method

a column generation based decomposition algorithm for a parallel machine just in time scheduling problem we propose a column generation based exact decomposition algorithm for the problem of scheduling n jobs with an unrestrictively large common due date on m identical parallel machines to minimize total weighted earliness and tardiness we first formulate the problem as an integer program then reformulate it using dantzig wolfe decomposition as a set partitioning problem with side constraints based on this set partitioning formulation a branch and bound exact solution algorithm is developed for the problem in the branch and bound tree each node is the linear relaxation problem of a set partitioning problem with side constraints this linear relaxation problem is solved by column generation approach where columns represent partial schedules on single machines and are generated by solving two single machine subproblems our computational results show that this decomposition algorithm is capable of solving problems with up to 60 jobs in reasonable cpu time

proximal point algorithms for nonsmooth convex optimization with fixed point constraints abstract the problem of minimizing the sum of nonsmooth convex objective functions defined on a real hilbert space over the intersection of fixed point sets of nonexpansive mappings onto which the projections cannot be efficiently computed is considered the use of proximal point algorithms that use the proximity operators of the objective functions and incremental optimization techniques is proposed for solving the problem with the focus on fixed point approximation techniques two algorithms are devised for solving the problem one blends an incremental subgradient method which is a useful algorithm for nonsmooth convex optimization with a halpern type fixed point iteration algorithm the other is based on an incremental subgradient method and the krasnosel ski mann fixed point algorithm it is shown that any weak sequential cluster point of the sequence generated by the halpern type algorithm belongs to the solution set of the problem and that there exists a weak sequential cluster point of the sequence generated by the krasnosel ski mann type algorithm which also belongs to the solution set numerical comparisons of the two proposed algorithms with existing subgradient methods for concrete nonsmooth convex optimization show that the proposed algorithms achieve faster convergence

parallel machine scheduling by column generation parallel machine scheduling problems concern the scheduling of n jobs on m machines to minimize some function of the job completion times if preemption is not allowed then most problems are not only np hard but also very hard from a practical point of view in this paper we show that strong and fast linear programming lower bounds can be computed for an important class of machine scheduling problems with additive objective functions characteristic of these problems is that on each machine the order of the jobs in the relevant part of the schedule is obtained through some priority rule to that end we formulate these parallel machine scheduling problems as a set covering problem with an exponential number of binary variables n covering constraints and a single side constraint we show that the linear programming relaxation can be solved efficiently by column generation because the pricing problem is solvable in pseudo polynomial time we display this approach on the problem of minimizing total weighted completion time on m identical machines our computational results show that the lower bound is singularly strong and that the outcome of the linear program is often integral moreover they show that our branch and bound algorithm that uses the linear programming lower bound outperforms the previously best algorithm

quadratic reformulations of nonlinear binary optimization problems very large nonlinear unconstrained binary optimization problems arise in a broad array of applications several exact or heuristic techniques have proved quite successful for solving many of these problems when the objective function is a quadratic polynomial however no similarly efficient methods are available for the higher degree case since high degree objectives are becoming increasingly important in certain application areas such as computer vision various techniques have been recently developed to reduce the general case to the quadratic one at the cost of increasing the number of variables by introducing additional auxiliary variables in this paper we initiate a systematic study of these quadratization approaches we provide tight lower and upper bounds on the number of auxiliary variables needed in the worst case for general objective functions for bounded degree functions and for a restricted class of quadratizations our upper bounds are constructive thus yielding new quadratization procedures finally we completely characterize all minimal quadratizations of negative monomials

novel generalized α methods for interfield parallel integration of heterogeneous structural dynamic systems a novel partitioned algorithm able to solve odes arising from transient structural dynamics is presented the spatial domain is partitioned into a set of disconnected subdomains owing to computational or physical considerations and continuity conditions of velocity at the interface are modelled using a dual schur formulation where lagrange multipliers represent reaction forces interface equations along with subdomain equations lead to a system of daes for which an interfield parallel procedure is developed the algorithm solves interface lagrange multipliers which are subsequently used to advance the solution in subdomains the proposed coupling algorithm that enables arbitrary email protected schemes to be coupled with different time steps in each subdomain is an extension of a method originally proposed by pegon and magonette thus subcycling permitting to deal also with stiff and nonstiff subsystems is allowed in detail the paper presents the convergence analysis of the novel interfield parallel scheme for linear single and two degrees of freedom systems because a multi degrees of freedom system is too difficult for a mathematical treatment however the insight gained from the analysis of these coupled problems and the consequent conclusions are confirmed by means of numerical experiments on a four degrees of freedom system

the symmetric quadratic traveling salesman problem in the quadratic traveling salesman problem a cost is associated with any three nodes traversed in succession this structure arises e g if the succession of two edges represents energetic conformations a change of direction or a possible change of transportation means in the symmetric case costs do not depend on the direction of traversal we study the polyhedral structure of a linearized integer programming formulation of the symmetric quadratic traveling salesman problem our constructive approach for establishing the dimension of the underlying polyhedron is rather involved but offers a generic path towards proving facetness of several classes of valid inequalities we establish relations to facets of the boolean quadric polytope exhibit new classes of polynomial time separable facet defining inequalities that exclude conflicting configurations of edges and provide a generic strengthening approach for lifting valid inequalities of the usual traveling salesman problem to stronger valid inequalities for the symmetric quadratic traveling salesman problem applying this strengthening to subtour elimination constraints gives rise to facet defining inequalities but finding a maximally violated inequality among these is np complete for the simplest comb inequality with three teeth the strengthening is no longer sufficient to obtain a facet preliminary computational results indicate that the new cutting planes may help to considerably improve the quality of the root relaxation in some important applications

an approximation algorithm for the generalized assignment problem the generalized assignment problem can be viewed as the following problem of scheduling parallel machines with costs each job is to be processed by exactly one machine processing jobj on machinei requires timep ij and incurs a cost ofc ij each machinei is available fort i time units and the objective is to minimize the total cost incurred our main result is as follows there is a polynomial time algorithm that given a valuec either proves that no feasible schedule of costc exists or else finds a schedule of cost at mostc where each machinei is used for at most 2t i time units we also extend this result to a variant of the problem where instead of a fixed processing timep ij there is a range of possible processing times for each machine job pair and the cost linearly increases as the processing time decreases we show that these results imply a polynomial time 2 approximation algorithm to minimize a weighted sum of the cost and the makespan i e the maximum job completion time we also consider the objective of minimizing the mean job completion time we show that there is a polynomial time algorithm that given valuesm andt either proves that no schedule of mean job completion timem and makespant exists or else finds a schedule of mean job completion time at mostm and makespan at most 2t

derandomizing approximation algorithms based on semidefinite programming remarkable breakthroughs have been made recently in obtaining approximate solutions to some fundamental np hard problems namely max cut max k cut max sat max dicut max bisection k vertex coloring maximum independent set etc all these breakthroughs involve polynomial time randomized algorithms based upon semidefinite programming a technique pioneered by goemans and williamson in this paper we give techniques to derandomize the above class of randomized algorithms thus obtaining polynomial time deterministic algorithms with the same approximation ratios for the above problems at the heart of our technique is the use of spherical symmetry to convert a nested sequence of n integrations which cannot be approximated sufficiently well in polynomial time to a nested sequence of just a constant number of integrations which can be approximated sufficiently well in polynomial time

on the accuracy of the kumaresan tufts method for estimating complex damped exponentials recently kumaresan and tufts kt presented a method for estimating the parameters of damped exponential waveforms in additive white noise the kt method uses singular value decomposition svd of the data matrix with truncation and backward prediction to improve the accuracy of the estimates the kt method was demonstrated to have a very good performance in comparison to traditional methods used for the same problem e g prony s method kumaresan and tufts also showed by numerical simulations that the variances of the estimates obtained by their method approaches the cramer rao lower bounds for selected test cases in this correspondence we provide a quantitative accuracy analysis of the kt method the analysis is based on first order taylor series approximations of the estimated parameters around their true values no assumptions are made on the number of data points used but it is assumed that the noise level is small enough for the first order approximations to be valid results of the analysis are illustrated by some numerical examples these results confirm the good performance of the kt method and show the effect of the user chosen parameters on the accuracy of the estimates

svd based information theoretic criteria for detection of the number of damped undamped sinusoids and their performance analysis following the information theoretic approach to model selection the authors develop criteria for detection of the number of damped undamped sinusoids these criteria are matched to the singular value decomposition svd based methods such as modified forward backward and forward backward linear prediction so well that the extra computations needed over and above those required for computing the svd are marginal next an analytical framework for analyzing the performance of these criteria is developed in the development of the analysis some approximations which become better for large signal to noise ratio are made simulations are used to verify the usefulness of the analysis and to compare the performance of the method with that of j j fuchs 1988

solving k cluster problems to optimality with semidefinite programming this paper deals with the computation of exact solutions of a classical np hard problem in combinatorial optimization the k cluster problem this problem consists in finding a heaviest subgraph with k nodes in an edge weighted graph we present a branch and bound algorithm that applies a novel bounding procedure based on recent semidefinite programming techniques we use new semidefinite bounds that are less tight than the standard semidefinite bounds but cheaper to get the experiments show that this approach is competitive with the best existing ones

new bounds for the identical parallel processor weighted flow time problem in 1964 eastman even and isaacs eei presented a polynomial time lower bound for the np hard problem of scheduling n jobs on m available and identical processors to minimize weighted flow time a general bound of which the eei bound is a special case is proposed four new bounds for the identical processor problem are given all of the new bounds can be applied to problems with variable processor ready times the eei bound is limited to problems where all processors are initially available at the same time two of the four new bounds are shown to dominate the eei bound the two other bounds are found to be effective for a particular problem class two polynomial time lower bounds for problems with nonidentical processors are introduced one bound is applicable to the uniform processor problem the other bound can be applied to the general processor problem no bounds have previously been proposed for these problems

convergence analysis of a parallel interfield method for heterogeneous simulations with dynamic substructuring summary in order to predict the dynamic response of a complex system decomposed by computational or physical considerations partitioned procedures of coupled dynamical systems are needed this paper presents the convergence analysis of a novel parallel interfield procedure for time integrating heterogeneous numerical physical subsystems typical of hardware in the loop and pseudo dynamic tests the partitioned method is an extension of the method originally proposed by gravouil and combescure which utilizes a domain decomposition enforcing the continuity of the velocity at interfaces in particular the merits of the new method which can couple arbitrary newmark schemes with different time steps in different subdomains and advance all the substructure states simultaneously are analysed in terms of accuracy and stability all theoretical results are derived for single and two degrees of freedom systems as a multi degree of freedom system is too difficult to analyse mathematically however the insight gained from the analysis of these coupled problems and the conclusions drawn are confirmed by means of the numerical simulation on a four degrees of freedom system copyright q 2008 john wiley sons ltd

lmi based robust mixed integer model predictive control for hybrid systems this paper proposes a linear matrix inequality lmi approach to mixed integer model predictive control mpc of uncertain hybrid systems with binary and real valued control inputs the stability c