grover s quantum algorithm applied to global optimization grover s quantum computational search procedure can provide the basis for implementing adaptive global optimization algorithms a brief overview of the procedure is given and a framework called grover adaptive search is set up a method of durr and hoyer and one introduced by the authors fit into this framework and are compared

experiments in quadratic 0 1 programming we present computational experience with a cutting plane algorithm for 0 1 quadratic programming without constraints our approach is based on a reduction of this problem to a max cut problem in a graph and on a partial linear description of the cut polytope

solving the 0 1 quadratic knapsack problem with a competitive quantum inspired evolutionary algorithm quadratic knapsack problem qkp extends the canonical simple knapsack problem where the value obtained by selecting a subset of objects is a function dependent not only on the value corresponding to individual objects selected but also on their pair wise selection qkp is np hard in stronger sense i e no pseudo polynomial time algorithm is known to exist which can solve qkp instances qkp has been studied intensively due to its simple structure yet challenging difficulty and numerous applications quantum inspired evolutionary algorithm qiea belongs to the class of evolutionary algorithms and exhibits behaviour of an estimation of distribution algorithm eda qiea provides a generic framework that has to be carefully tailored for a given problem to obtain an effective implementation thus several forms of qiea exist in the literature these have been successfully applied on many hard problems a new qiea qiea psa is proposed with improved exploration and exploitation capabilities computational experiments on these benchmarks show that qiea psa is improved significantly both in terms of the quality of solutions and speed of convergence on several benchmark qkp instances the ideas incorporated are general enough and can be utilized with advantage on other similar and not so similar problems

lagrangean methods for the 0 1 quadratic knapsack problem abstract it is well known that the lagrangean decomposition provides better bounds than the lagrangean relaxation does nevertheless the lagrangean decomposition bound is harder to compute than the lagrangean relaxation bound thus one might wonder what is the best lagrangean method to use in a branch and bound algorithm in this paper we give an answer to such a question for the 0 1 quadratic knapsack problem we first study the lagrangean decomposition for this problem and give new necessary optimality conditions for the dual problem which allow us to elaborate a heuristic method for solving the lagrangean decomposition dual problem we then introduce this method in chaillou hansen mahieu s branch and bound algorithm where upper bounds were computed by lagrangean relaxation

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

wavelets for waveform coding of digital symbols a wavelet based coder decoder codec structure is defined for baseband waveform coding numerical results for bandwidth efficiency are given and a comparison between several different wavelets is presented moreover it is shown that wavelets obey the nyquist pulse shaping condition and provide a unified framework for analog pulse shaping concepts of communications

mildly dissipative nonlinear timoshenko systems global existence and exponential stability we consider nonlinear systems of timoshenko type in a one dimensional bounded domain the system has a dissipative mechanism being present only in the equation for the rotation angle it is a damping effect through heat conduction the global existence of small smooth solutions as well as the exponential stability are investigated

improving the efficiency of the branch and bound algorithm for integer programming based on flatness information abstract this paper describes a strategy for defining priorities for the branching variables in a branch and bound algorithm the strategy is based on shape information about the polyhedron over which we are optimizing this information is related to measures of the integer width as provided by the so called flatness theorem our selection rule uses that knowledge to define branching priorities on the variables computational results with simulated small to medium size integer problems are presented as well with multi knapsack problems these show savings of about 40 in cpu time as well as in nodes generated in the search tree and compare favorably with respect to other standard branching rules

an efficient mean field approach to the set covering problem a mean field feedback artificial neural network ann algorithm is developed and explored for the set covering problem a convenient encoding of the inequality constraints is achieved by means of a multilinear penalty function an approximate energy minimum is obtained by iterating a set of mean field equations in combination with annealing the approach is numerically tested against a set of publicly available test problems with sizes ranging up to 5 103 rows and 106 columns when comparing the performance with exact results for sizes where these are available the approach yields results within a few percent from the optimal solutions comparisons with other approximate methods also come out well in particular given the very low cpu consumption required typically a few seconds arbitrary problems can be processed using the algorithm via a public domain server 2001 elsevier science b v less

path relinking for unconstrained binary quadratic programming abstract this paper presents two path relinking algorithms to solve the unconstrained binary quadratic programming ubqp problem one is based on a greedy strategy to generate the relinking path from the initial solution to the guiding solution and the other operates in a random way we show extensive computational results on five sets of benchmarks including 31 large random ubqp instances and 103 structured instances derived from the maxcut problem comparisons with several state of the art algorithms demonstrate the efficacy of our proposed algorithms in terms of both solution quality and computational efficiency it is noteworthy that both algorithms are able to improve the previous best known results for almost 40 percent of the 103 maxcut instances

a simplified binary artificial fish swarm algorithm for 0 1 quadratic knapsack problems this paper proposes a simplified binary version of the artificial fish swarm algorithm s bafsa for solving 0 1 quadratic knapsack problems this is a combinatorial optimization problem which arises in many fields of optimization in s bafsa trial points are created by using crossover and mutation in order to make the points feasible a random heuristic drop item procedure is used the heuristic add item is also implemented to improve the quality of the solutions and a cyclic reinitialization of the population is carried out to avoid convergence to non optimal solutions to enhance the accuracy of the solution a swap move heuristic search is applied on a predefined number of points the method is tested on a set of benchmark 0 1 knapsack problems

asymptotic stability of a viscoelastic problem with balakrishnantaylor damping and time varying delay a viscoelastic problem with balakrishnantaylordamping and time varying delay of the form utt a bu2 u ut u 0tg ts u s ds 1f1 ut x t 2f2 ut x t t 0is considered we prove a general stability result for the equation without the condition 2 0 by establishing some lyapunov functionals which are equivalent to the energy of the equation instead of multiplier technique and using some properties of convex functions

a stability result of a timoshenko system with a delay term in the internal feedback abstract in this paper we consider a timoshenko system with a delay term in the feedback and prove a stability result the beam is clamped at the endpoints and has in addition to an internal damping a feedback with a delay under an appropriate assumption on the weights of the two feedbacks we prove the well posedness of the system and establish an exponential decay result for the case of equal speed wave propagation

general decay of the solution energy in a viscoelastic equation with a nonlinear source abstract in a bounded domain we consider u t t u 0 t g t u d u u where 0 and g is a nonnegative and decaying function we prove that for certain class of relaxation functions and certain initial data the rate of decay of energy is similar to that of g this result improves earlier ones in the literature in which only the exponential and polynomial decay rates are considered

using modifications to grover s search algorithm for quantum global optimization we study the problem of finding a global optimal solution to discrete optimization problems using a heuristic based on quantum computing methods knowledge of quantum computing ideas is not necessary to read this paper we focus on a successful quantum computing method introduced by baritompa bulger and wood that we refer to as the bbw algorithm and develop two modifications first we modify the bbw algorithm to achieve a dramatic speedup that lets us extend the known bbw static schedule from 33 to 43 points thereby increasing its applicability we further modify it by converting it from a static method to a dynamic one experimental results show the value of this latter modification

asymptotic stability of a problem with balakrishnantaylor damping and a time delay in this paper we investigate the asymptotic stability of the viscoelastic kirchhoff equation with balakrishnantaylor damping and a delay term we establish general energy decay result by suitable lyapunov functionals

stability of timoshenko systems with past history we consider vibrating systems of timoshenko type with past history acting only in one equation we show that the dissipation given by the history term is strong enough to produce exponential stability if and only if the equations have the same wave speeds otherwise the corresponding system does not decay exponentially as time goes to infinity in the case that the wave speeds of the equations are different which is more realistic from the physical point of view we show that the solution decays polynomially to zero with rates that can be improved depending on the regularity of the initial data

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

stabilization of second order evolution equations with unbounded feedback with time dependent delay we consider abstract second order evolution equations with unbounded feedback with time varying delay existence results are obtained under some realistic assumptions we prove the exponential decay under some conditions by introducing an abstract lyapunov functional our abstract framework is applied to the wave to the beam and to the plate equations with boundary delays

pure adaptive search for finite global optimization pure adaptive search is a stochastic algorithm which has been analyzed for continuous global optimization when a uniform distribution is used in pas it has been shown to have complexity which is linear in dimension we define strong and weak variations of pas in the setting of finite global optimization and prove analogous results in particular for then dimensional lattice 1 k n the expected number of iterations to find the global optimum is linear inn many discrete combinatorial optimization problems although having intractably large domains have quite small ranges the strong version of pas for all problems and the weak version of pas for a limited class of problems has complexity the order of the size of the range

on decay and blow up of the solution for a viscoelastic wave equation with boundary damping and source terms abstract in this paper we consider the decay and blow up properties of a viscoelastic wave equation with boundary damping and source terms we first extend the decay result for the case of linear damping obtained by lu et al on a viscoelastic equation with nonlinear boundary damping and source terms global existence and decay of the solution nonlinear analysis real world applications 12 1 2011 295 303 to the nonlinear damping case under weaker assumption on the relaxation function g t then we give an exponential decay result without the relation between g t and g t for the linear damping case provided that g l 1 0 is small enough finally we establish two blow up results one is for certain solutions with nonpositive initial energy as well as positive initial energy for both the linear and nonlinear damping cases the other is for certain solutions with arbitrarily positive initial energy for the linear damping case

stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks in this paper we consider in a bounded and smooth domain the wave equation with a delay term in the boundary condition we also consider the wave equation with a delayed velocity term and mixed dirichlet neumann boundary condition in both cases under suitable assumptions we prove exponential stability of the solution these results are obtained by introducing suitable energies and by using some observability inequalities if one of the above assumptions is not satisfied some instability results are also given by constructing some sequences of delays for which the energy of some solutions does not tend to zero

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

a cutting plane approach to the edge weighted maximal clique problem we investigated the computational performance of a cutting plane algorithm for the problem of determining a maximal subclique in an edge weighted complete graph our numerical results are contrasted with reports on closely related problems for which cutting plane approaches perform well in instances of moderate size somewhat surprisingly we find that our approach already in the case of n 15 or n 25 nodes in the underlying graph typically neither produces an integral solution nor yields a good approximation to the true optimal objective function value this result seems to shed some doubt on the universal applicability of cuttingplane approaches as an efficient means to solve linear 0 1 programming problems of moderate size

brief paper an integer programming approach to optimal control problems in context sensitive probabilistic boolean networks a boolean network is one of the models of biological networks such as gene regulatory networks and has been extensively studied in particular a probabilistic boolean network pbn is well known as an extension of boolean networks but in the existing methods to solve the optimal control problem of pbns it is necessary to compute the state transition diagram with 2 n nodes for a given pbn with n states to avoid this computation an integer programming based approach is proposed for a context sensitive pbn cs pbn which is a general form of pbns in the proposed method a cs pbn is transformed into a linear system with binary variables and the optimal control problem is reduced to an integer linear programming problem by a numerical example the effectiveness of the proposed method is shown

one pass heuristics for large scale unconstrained binary quadratic problems abstract many significant advances have been made in recent years for solving unconstrained binary quadratic programs uqp as a result the size of problem instances that can be efficiently solved has grown from a hundred or so variables a few years ago to 2000 or 3000 variables today these advances have motivated new applications of the model which in turn have created the need to solve even larger problems in response to this need we introduce several new one pass heuristics for solving very large versions of this problem our computational experience on problems of up to 9000 variables indicates that these methods are both efficient and effective for very large problems the significance of problems of this size is that they not only open the door to solving a much wider array of real world problems but also that the standard linear mixed integer formulations of the nonlinear models involve over 40 000 000 variables and three times that many constraints our approaches can be used as stand alone solution methods or they can serve as procedures for quickly generating high quality starting points for other more sophisticated methods

wavelet based representations for a class of self similar signals with application to fractal modulation a potentially important family of self similar signals based upon a deterministic scale invariance characterization is introduced these signals which are referred to as dy homogeneous signals because they generalize the well known homogeneous functions have highly convenient representations in terms of orthonormal wavelet bases in particular wavelet representations can be exploited to construct orthonormal self similar bases for these signals the spectral and fractal characteristics of dy homogeneous signals make them appealing candidates for use in a number of applications as one potential example their use in a communications based context is considered specifically a strategy for embedding information into a dy homogeneous waveform on multiple time scales is developed this multirate modulation strategy called fractal modulation is potentially well suited for use with noisy channels of simultaneously unknown duration and bandwidth

formulations and valid inequalities for the node capacitated graph partitioning problem we investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights in each subset of the partition the objective is to minimize the sum of the costs of the edges between the subsets of the partition this problem has a variety of applications for instance in the design of electronic circuits and devices we present alternative integer programming formulations for this problem and discuss the links between these formulations having chosen to work in the space of edges of the multicut we investigate the convex hull of incidence vectors of feasible multicuts in particular several classes of inequalities are introduced and their strength and robustness are analyzed as various problem parameters change

pure adaptive search in monte carlo optimization pure adaptive search constructs a sequence of points uniformly distributed within a corresponding sequence of nested regions of the feasible space at any stage the next point in the sequence is chosen uniformly distributed over the region of feasible space containing all points that are equal or superior in value to the previous points in the sequence we show that for convex programs the number of iterations required to achieve a given accuracy of solution increases at most linearly in the dimension of the problem this compares to exponential growth in iterations required for pure random search

an application of combinatorial optimization to statistical physics and circuit layout design we study the problem of finding ground states of spin glasses with exterior magnetic field and the problem of minimizing the number of vias holes on a printed circuit board or contacts on a chip subject to pin preassignments and layer preferences the former problem comes up in solid state physics and the latter in very large scale integrated vlsi circuit design and in printed circuit board design both problems can be reduced to the max cut problem in graphs based on a partial characterization of the cut polytope we design a cutting plane algorithm and report on computational experience with it our method has been used to solve max cut problems on graphs with up to 1 600 nodes

unbounded knapsack problem dynamic programming revisited abstract we present eduk an efficient dynamic programming algorithm for the unbounded knapsack problem it is based primarily on a new and useful dominance relation called threshold dominance which is a strict generalization of all the previously known dominance relations we show that combining it with a sparse representation of the iteration domain and the periodicity property leads to a drastic reduction of the solution space we present computational experiments with various data instances to validate our ideas and demonstrate the efficiency of eduk vis a vis the well known exact algorithm mtu2

on linear programs with random costs we consider linear programs in which the objective function cost coefficients are independent non negative random variables and give upper bounds for the random minimum cost one application shows that for quadratic assignment problems with such costs certain branch and bound algorithms usually take more than exponential time

an augmented lagrangian fish swarm based method for global optimization this paper presents an augmented lagrangian methodology with a stochastic population based algorithm for solving nonlinear constrained global optimization problems the method approximately solves a sequence of simple bound global optimization subproblems using a fish swarm intelligent algorithm a stochastic convergence analysis of the fish swarm iterative process is included numerical results with a benchmark set of problems are shown including a comparison with other stochastic type algorithms

an evolutionary heuristic for quadratic 0 1 programming abstract in this paper we present a heuristic algorithm for the well known unconstrained quadratic 0 1 programming problem the approach is based on combining solutions in a genetic paradigm and incorporates intensification algorithms used to improve solutions and speed up the method extensive computational experiments on instances with up to 500 variables are presented and we compare our approach both with powerful heuristic and exact algorithms from the literature establishing the effectiveness of the method in terms of solutions quality and computing time

general decay of the solution for a viscoelastic wave equation with a time varying delay term in the internal feedback in this paper we consider a viscoelastic wave equation with a time varying delay term the coefficient of which is not necessarily positive by introducing suitable energy and lyapunov functionals under suitable assumptions we establish a general energy decay result from which the exponential and polynomial types of decay are only special cases

a dynamic programming based reduction procedure for the multidimensional 0 1 knapsack problem abstract this paper presents a preprocessing procedure for the 0 1 multidimensional knapsack problem first a non increasing sequence of upper bounds is generated by solving lp relaxations then a non decreasing sequence of lower bounds is built using dynamic programming the comparison of the two sequences allows either to prove that the best feasible solution obtained is optimal or to fix a subset of variables to their optimal values in addition a heuristic solution is obtained computational experiments with a set of large scale instances show the efficiency of our reduction scheme particularly it is shown that our approach allows to reduce the cpu time of a leading commercial software

linear programming for the 0 1 quadratic knapsack problem abstract in this paper we consider the quadratic knapsack problem which consists in maximizing a positive quadratic pseudo boolean function subject to a linear capacity constraint we propose a new method for computing an upper bound this method is based on the solution of a continuous linear program constructed by adding to a classical linearization of the problem some constraints rebundant in 0 1 variables but nonredundant in continuous variables the obtained upper bound is better than the bounds given by other known methods we also propose an algorithm for computing a good feasible solution this algorithm is an elaboration of the heuristic methods proposed by chaillou hansen and mahieu and by gallo hammer and simeone the relative error between this feasible solution and the optimum solution is generally less than 1 we show how these upper and lower bounds can be efficiently used to determine the values of some variables at the optimum finally we propose a branch and bound algorithm for solving the quadratic knapsack problem and report extensive computational tests

energy decay for timoshenko systems of memory type abstract linear systems of timoshenko type equations for beams including a memory term are studied the exponential decay is proved for exponential kernels while polynomial kernels are shown to lead to a polynomial decay the optimality of the results is also investigated

boundary stabilization of solutions of a nonlinear system of timoshenko type in this paper we are concerned with a multidimensional timoshenko system subjected to boundary conditions of memory type we establish general rate decay results the usual exponential and polynomial decay rates are only special cases

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

uniform decay in a timoshenko type system with past history abstract fernandez sare and rivera h d fernandez sare j e munoz rivera stability of timoshenko systems with past history j math anal appl 339 1 2008 482 502 considered the following timoshenko type system 1 t t k x x 0 2 t t b x x 0 g t x x t s d s k x 0 where g is a positive differentiable exponentially decaying function they established an exponential decay result in the case of equal wave speed propagation and a polynomial decay result in the case of nonequal wave speed propagation in this paper we study the same system for g decaying polynomially and prove polynomial stability results for the equal and nonequal wave speed propagation our results are established under conditions on the relaxation function weaker than those in h d fernandez sare j e munoz rivera stability of timoshenko systems with past history j math anal appl 339 1 2008 482 502

a new upper bound for the 0 1 quadratic knapsack problem the 0 1 quadratic knapsack problem qkp consists in maximizing a positive quadratic pseudo boolean function subject to a linear capacity constraint we present in this paper a new method based on lagrangian decomposition for computing an upper bound of qkp we report computational experiments which demonstrate the sharpness of the bound relative error very often less than 1 for large size instances up to 500 variables

the boolean quadric polytope some characteristics facets and relatives we study unconstrained quadratic zero one programming problems havingn variables from a polyhedral point of view by considering the boolean quadric polytope qpn inn n 1 2 dimensions that results from the linearization of the quadratic form we show that qpn has a diameter of one descriptively identify three families of facets of qpn and show that qpn is symmetric in the sense that all facets of qpn can be obtained from those that contain the origin by way of a mapping the naive linear programming relaxation qpnlp of qpn is shown to possess the trubin property and its extreme points are shown to be 0 1 2 1 valued furthermore o n3 facet defining inequalities of qpn suffice to cut off all fractional vertices of qpnlp whereas the family of facets described by us has at least o 3n members the problem is also studied for sparse quadratic forms i e when several or many coefficients are zero and conditions are given for the previous results to carry over to this case polynomially solvable problem instances are discussed and it is shown that the known polynomiality result for the maximization of nonnegative quadratic forms can be obtained by simply rounding the solution to the linear programming relaxation in the case that the graph induced by the nonzero coefficients of the quadratic form is series parallel a complete linear description of the associated boolean quadric polytope is given the relationship of the boolean quadric polytope associated to sparse quadratic forms with the vertex packing polytope is discussed as well

cutting planes for rlt relaxations of mixed 0 1 polynomial programs the reformulation linearization technique due to sherali and adams can be used to construct hierarchies of linear programming relaxations of mixed 0 1 polynomial programs as one moves up the hierarchy the relaxations grow stronger but the number of variables increases exponentially we present a procedure that generates cutting planes at any given level of the hierarchy by optimally weakening linear inequalities that are valid at any given higher level computational experiments conducted on instances of the quadratic knapsack problem indicate that the cutting planes can close a significant proportion of the integrality gap

performance of wavelet packet division multiplexing in impulsive and gaussian noise wavelet packet division multiplexing wpdm is a high capacity flexible and robust multiple signal transmission technique in which the message signals are waveform coded onto wavelet packet basis functions for transmission we derive an expression for the probability of error for a wpdm scheme in the presence of both impulsive and gaussian noise sources and demonstrate that wpdm can provide greater immunity to impulsive noise than both a time division multiplexing scheme and an orthogonal frequency division multiplexing scheme

dual mean field search for large scale linear and quadratic knapsack problems abstract an implementation of mean field annealing to deal with large scale linear and non linear binary optimization problems is given mean field annealing is based on the analogy between combinatorial optimization and interacting physical systems at thermal equilibrium specifically a mean field approximation of the boltzmann distribution given by a lagrangian that encompass the objective function and the constraints is calculated the original discrete task is in this way transformed into a continuous variational problem in our version of mean field annealing no temperature parameter is used but a good starting point in the dual space is given by a thermodynamic limit argument the method is tested in linear and quadratic knapsack problems with sizes that are considerably larger than those used in previous studies of mean field annealing dual mean field annealing is capable to find high quality solutions in running times that are orders of magnitude shorter than state of the art algorithms moreover as may be expected for a mean field theory the solutions tend to be more accurate as the number of variables grow

constrained 0 1 quadratic programming basic approaches and extensions abstract we describe the simplest technique to tackle 0 1 quadratic programs with linear constraints among those that turn out to be successful in practice this method is due to and familiar to the quadratic assignment experts even if it took some time to realize that most approaches to the problem could be interpreted in these terms whereas it does not appear to be widely known outside this community since the technique is completely general and is by far the most successful one in several other cases such as quadratic knapsack we illustrate it in its full generality pointing out its relationship to lagrangian and linear programming relaxations and discussing further extensions we believe that this method should be in the background of every practitioner in combinatorial optimization

an effective branch and bound algorithm for convex quadratic integer programming we present a branch and bound algorithm for minimizing a convex quadratic objective function over integer variables subject to convex constraints in a given node of the enumeration tree corresponding to the fixing of a subset of the variables a lower bound is given by the continuous minimum of the restricted objective function we improve this bound by exploiting the integrality of the variables using suitably defined lattice free ellipsoids experiments show that our approach is very fast on both unconstrained problems and problems with box constraints the main reason is that all expensive calculations can be done in a preprocessing phase while a single node in the enumeration tree can be processed in linear time in the problem dimension

refining the phase transition in combinatorial search abstract many recent studies have identified phase transitions from under to overconstrained instances in classes of constraint satisfaction search problems and their relation to search cost for example cases that are difficult to solve with a variety of search methods are concentrated near these transitions these studies show that a simple parameter describing the problem structure predicts the difficulty of solving the problem on average however this prediction is associated with a large variance and depends on the somewhat arbitrary choice of the problem class thus these results are of limited direct use for individual instances to help address this limitation additional parameters describing problem structure as well as heuristic effectiveness are introduced these are shown to reduce the variation in some cases this also provides further insight into the nature of intrinsically hard search problems

min cut clustering we describe a decomposition framework and a column generation scheme for solving a min cut clustering problem the subproblem to generate additional columns is itself an np hard mixed integer programming problem we discuss strong valid inequalities for the subproblem and describe some efficient solution strategies computational results on compiler construction problems are reported

an example on the effect of time delays in boundary feedback stabilization of wave equations this note is concerned with the erect of time delays in boundary feedback stabilization schemes for wave equations the question to be addressed is whether such delays can destabilize a system which is uniformly asymptotically stable in the absence of delays

lagrangean decomposition a model yielding stronger lagrangean bounds given a mixed integer programming problem with two matrix constraints it is possible to define a lagrangean relaxation such that the relaxed problem decomposes additively into two subproblems each having one of the two matrices of the original problem as its constraints there is one lagrangean multiplier per variable we prove that the optimal value of this new lagrangean dual dominates the optimal value of the lagrangean dual obtained by relaxing one set of constraints and give a necessary condition for a strict improvement we show on an example that the resulting bound improvement can be substantial we show on a complex practical problem how lagrangean decomposition may help uncover hidden special structures and thus yield better solution methodology

pure adaptive search in global optimization pure adaptive seach iteratively constructs a sequence of interior points uniformly distributed within the corresponding sequence of nested improving regions of the feasible space that is at any iteration the next point in the sequence is uniformly distributed over the region of feasible space containing all points that are strictly superior in value to the previous points in the sequence the complexity of this algorithm is measured by the expected number of iterations required to achieve a given accuracy of solution we show that for global mathematical programs satisfying the lipschitz condition its complexity increases at mostlinearly in the dimension of the problem

an exact method based on lagrangian decomposition for the 0 1 quadratic knapsack problem abstract the 0 1 quadratic knapsack problem qkp consists in maximizing a quadratic pseudo boolean function with positive coefficients subject to a linear capacity constraint in this paper we present an exact method to solve this problem this method makes use of the computation of an upper bound for qkp which is derived from lagrangian decomposition it allows us to find the optimum of instances with up to 150 variables whatever their density and with up to 300 variables for medium and low density

general decay rate for weak viscoelastic wave equation with balakrishnan taylor damping and time varying delay abstract a weak viscoelastic wave equation with balakrishnan taylor damping and internal time varying delay in a bounded domain is considered the balakrishnan taylor damping appears in the flutter panel equation and the spillover problem which was initially proposed by balakrishnan and taylor in 1989 the presence of delay may be a source of instability under appropriate assumptions on the source term with the relaxation function and certain initial data and by adopting the perturbed energy method we establish general decay estimate for the energy which depends on the behavior of the relation function and which is not necessarily decaying in a polynomial or exponential fashion

boundary control of the timoshenko beam it is shown that the timoshenko beam can be uniformly stabilized by means of a boundary control a numerical study on the spectrum is also presented

parametric convex quadratic relaxation of the quadratic knapsack problem abstract we consider a parametric convex quadratic programming cqp relaxation for the quadratic knapsack problem qkp this relaxation maintains partial quadratic information from the original qkp by perturbing the objective function to obtain a concave quadratic term the nonconcave part generated by the perturbation is then linearized by a standard approach that lifts the problem to matrix space we present a primal dual interior point method to optimize the perturbation of the quadratic function in a search for the tightest upper bound for the qkp we prove that the same perturbation approach when applied in the context of semidefinite programming sdp relaxations of the qkp cannot improve the upper bound given by the corresponding linear sdp relaxation the result also applies to more general integer quadratic problems finally we propose new valid inequalities on the lifted matrix variable derived from cover and knapsack inequalities for the qkp and present separation problems to generate cuts for the current solution of the cqp relaxation our best bounds are obtained alternating between optimizing the parametric quadratic relaxation over the perturbation and applying cutting planes generated by the valid inequalities proposed

asymptotic behavior of the quadratic knapsack problem abstract we study the quadratic knapsack problem on instances where the profits are independent random variables defined on the interval 0 1 and the knapsack capacity is proportional to the number of items we assume that the weights are arbitrary numbers from the interval 0 1 we show asymptotically that the objective value of a very easy heuristic is not far away from the optimal solution more specifically we show that the ratio of the optimal solution and the objective value of this heuristic almost surely tends to 1 as the size of the knapsack instance tends to infinity as a consequence using randomly generated instances following this scheme seems to be inappropriate for studying the performance of heuristics and to some extend exact methods however such instances are frequently used in the literature for this purpose additionally we introduce a class of test instances based on hidden cliques for which finding a good solution is much harder we support this by theoretical observations as well as by performing computational experiments

on the control of a viscoelastic damped timoshenko type system abstract in this paper we consider the following timoshenko system tt x x 0 0 1 0 tt xx 0 t g t xx d x 0 0 1 0 with dirichlet boundary conditions where g is a positive nonincreasing function we establish an exponential and polynomial decay results with weaker conditions on g than those required in f ammar khodja a benabdallah j e munoz rivera r racke energy decay for timoshenko systems of memory type j differ equations 194 2003 82 115

on behaviour of solutions for a nonlinear viscoelastic equation with variable exponent nonlinearities abstract this paper deals with a viscoelastic wave equation with variable exponent nonlinearities subject to nonlinear boundary feedback under appropriate conditions a general decay result associated to solution energy is proved it is also shown that regarding arbitrary positive initial energy solutions blow up in a finite time

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

a re examination of the basic postulates of thermomechanics this paper is mainly concerned with a re examination of the basic postulates and the consequent procedure for the construction of the constitutive equations of material behaviour in thermomechanics however the implication of the basic postulates and the significance of the related procedure for the development of the constitutive equations is also illustrated in some detail in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed more specifically after briefly examining the nature of the basic equations of motion for a system of particles within the scope of the classical newtonian mechanics the basic postulates of the purely mechanical theory for a continuum including its specialization for a rigid body is re examined this includes some differences from the usual procedure on the subject next thermal variables are introduced and after observing a useful analogy between the thermal and mechanical variables a discussion of a theory of heat or a purely thermal theory is provided which differs from the usual development in the classical thermodynamics a detailed application of the latter development is then made to the problem of heat flow in a stationary rigid solid using several different and well motivated constitutive equations special cases of these include linearized theories of the classical heat flow by conduction and of heat flow transmitted as thermal waves the remainder of the paper is concerned with thermal mechanical theory of deformable media along with discussions of a number of related issues on the subject

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

a decomposition method for quadratic zero one programming this paper proposes a decomposition method to compute a lower bound for unconstrained quadratic zero one minimization first we show that any quadratic function can be expressed as a sum of particular quadratic functions whose minima can be computed by a simple branch and bound algorithm then assuming some hypothesis we prove that among all possible decompositions the best one can be found by a lagrangian decomposition method moreover we show that our algorithm gives at least the roof dual bound and should give better results in practice eventually computational results and comparison with pardalos and rodgers algorithm demonstrate the efficiency of our method for medium size problems up to 100 variables

a hybrid metaheuristic approach to solving the ubqp problem this paper presents a hybrid metaheuristic approach hma for solving the unconstrained binary quadratic programming ubqp problem by incorporating a tabu search procedure into the framework of evolutionary algorithms the proposed approach exhibits several distinguishing features including a diversification based combination operator and a distance and quality based replacement criterion for pool updating the proposed algorithm is able to easily obtain the best known solutions for 31 large random instances up to 7000 variables which no previous algorithm has done and find new best solutions for three of nine instances derived from the set partitioning problem demonstrating the efficacy of our proposed algorithm in terms of both solution quality and computational efficiency furthermore some key elements and properties of the hma algorithm are also analyzed

timoshenko systems with indefinite damping abstract we consider the timoshenko system in a bounded domain 0 l r 1 the system has an indefinite damping mechanism i e with a damping function a a x possibly changing sign present only in the equation for the rotation angle we shall prove that the system is still exponentially stable under the same conditions as in the positive constant damping case and provided a 0 l a x d x 0 and a a l 2 for small enough the decay rate will be described explicitly in the arguments we shall also give a new proof of exponential stability for the constant case a a moreover we give a precise description of the decay rate and demonstrate that the system has the spectrum determined growth sdg property i e the type of the induced semigroup coincides with the spectral bound for its generator

an extended formulation approach to the edge weighted maximal clique problem we consider an extended formulation approach to the edge weighted maximal clique problem the problem is formulated by using additional variables for the set of nodes with the natural variables for the set of edges we show that the proposed formulation is superior to the natural formulation both theoretically and practically by using the projection technique we can also derive new classes of facet defining inequalities for the lower dimensional polytope of the natural variables computational results are reported

minimization of a quadratic pseudo boolean function abstract we present a branch and bound algorithm for minimizing a quadratic pseudo boolean function f x at each node of the search tree the lower bound is computed in three phases and is equal to b 1 b 2 b 3 computation of b 1 is based upon roof duality b 2 uses the characterization of some positive quadratic posiforms associated with the directed cycles of the implication graph of aspvall plass and tarjan and b 3 is computed by searching in a posiform of degree 4 some subfunctions which cannot be equal to zero these subfunctions are found by using the notion of implication between literals computational results on several hundred test problems with up to 100 variables demonstrate the efficiency of this lower bound

on the supermodular knapsack problem in this paper we introduce binary knapsack problems where the objective function is nonlinear and investigate their lagrangean and continuous relaxations some of our results generalize previously known theorems concerning linear and quadratic knapsack problems we investigate in particular the case in which the objective function is supermodular under this hypothesis although the problem remains np hard we show that its lagrangean dual and its continuous relaxation can be solved in polynomial time we also comment on the complexity of recognizing supermodular functions the particular case in which the knapsack constraint is of the cardinality type is also addressed and some properties of its optimal value as a function of the right hand side are derived

a self adaptive binary differential evolution algorithm for large scale binary optimization problems a new binary variant of the de algorithm is presented a new approach to design search strategies for the binary de algorithms is suggested the proposed algorithm is implemented and tested on modern benchmark problems and high dimensional knapsack problems the performance of the proposed algorithm is compared against some recently presented binary algorithms this study proposes a new self adaptive binary variant of a differential evolution algorithm based on measure of dissimilarity and named sabde it uses an adaptive mechanism for selecting how new trial solutions are generated and a chaotic process for adapting parameter values sabde is compared against a number of existing state of the art algorithms on a set of benchmark problems including high dimensional knapsack problems with up to 10 000 dimensions as well as on the 15 learning based problems of the congress on evolutionary computation cec 2015 experimental results reveal that the proposed algorithm performs competitively and in some cases is superior to the existing algorithms

average performance of greedy heuristics for the integer knapsack problem abstract this paper derives a lower bound on the average performance of a total value greedy heuristic for the integer knapsack problem this heuristic selects items in order of their maximum possible contribution to the solution value at each stage we show that as for the worst case bound the average performance bound for the total value heuristic dominates the corresponding bound for the density ordered greedy heuristic

a dual decomposition approach to feature correspondence in this paper we present a new approach for establishing correspondences between sparse image features related by an unknown nonrigid mapping and corrupted by clutter and occlusion such as points extracted from images of different instances of the same object category we formulate this matching task as an energy minimization problem by defining an elaborate objective function of the appearance and the spatial arrangement of the features optimization of this energy is an instance of graph matching which is in general an np hard problem we describe a novel graph matching optimization technique which we refer to as dual decomposition dd and demonstrate on a variety of examples that this method outperforms existing graph matching algorithms in the majority of our examples dd is able to find the global minimum within a minute the ability to globally optimize the objective allows us to accurately learn the parameters of our matching model from training examples we show on several matching tasks that our learned model yields results superior to those of state of the art methods

lagrangian decomposition of block separable mixed integer all quadratic programs the purpose of this paper is threefold first we propose splitting schemes for reformulating non separable problems as block separable problems second we show that the lagrangian dual of a block separable mixed integer all quadratic program miqqp can be formulated as an eigenvalue optimization problem keeping the block separable structure finally we report numerical results on solving the eigenvalue optimization problem by a proximal bundle algorithm applying lagrangian decomposition the results indicate that appropriate block separable reformulations of miqqps could accelerate the running time of dual solution algorithms considerably

the nonlinear knapsack problem algorithms and applications abstract we present a survey of algorithms and applications for the nonlinear knapsack problem or the nonlinear resource allocation problem in its most general form the nonlinear knapsack problem will be defined as a nonlinear optimization problem with just one constraint bounds on the variables and in some cases a set of specially structured constraints such as generalized upper bounds gubs this problem is encountered either directly or as a subproblem in a variety of applications including production planning financial modeling stratified sampling and capacity planning in manufacturing health care and computer networks by taking advantage of the special structure of the problem efficient solution methods can be developed problem classes addressed here include continuous and integer problems convex and nonconvex problems separable and nonseparable problems and problems with additional specially structured constraints

a tight linearization and an algorithm for zero one quadratic programming problems this paper is concerned with the solution of linearly constrained zero one quadratic programming problems problems of this kind arise in numerous economic location decision and strategic planning situations including capital budgeting facility location quadratic assignment media selection and dynamic set covering a new linearization technique is presented for this problem which is demonstrated to yield a tighter continuous or linear programming relaxation than is available through other methods an implicit enumeration algorithm which uses lagrangian relaxation benders cutting planes and local explorations is designed to exploit the strength of this linearization computational experience is provided to demonstrate the usefulness of the proposed linearization and algorithm

ruling out ptas for graph min bisection dense k subgraph and bipartite clique assuming that np not subseteq cap epsilon 0 bptime 2 n epsilon we show that graph min bisection dense k subgraph and bipartite clique have no polynomial time approximation scheme ptas we give a reduction from the minimum distance of code mdc problem starting with an instance of mdc we build a quasi random probabilistically checkable proof pcp that suffices to prove the desired inapproximability results in a quasi random pcp the query pattern of the verifier looks random in a certain precise sense among the several new techniques we introduce the most interesting one gives a way of certifying that a given polynomial belongs to a given linear subspace of polynomials as is important for our purpose the certificate itself happens to be another polynomial and it can be checked probabilistically by reading a constant number of its values

global nonexistence of solutions for a nonlinear wave equation with time delay and acoustic boundary conditions abstract we consider a quasilinear wave equation u t t u t d i v u 2 u d i v u t 2 u t a u t m 2 u t 1 u t x t 2 u t x t b u p 2 u a b 0 associated with initial and dirichlet boundary conditions at one part and acoustic boundary conditions at another part respectively we prove under suitable conditions on m p and for negative initial energy a global nonexistence of solutions

a fast parametric maximum flow algorithm and applications the classical maximum flow problem sometimes occurs in settings in which the arc capacities are not fixed but are functions of a single parameter and the goal is to find the value of the parameter such that the corresponding maximum flow or minimum cut satisfies some side condition finding the desired parameter value requires solving a sequence of related maximum flow problems in this paper it is shown that the recent maximum flow algorithm of goldberg and tarjan can be extended to solve an important class of such parametric maximum flow problems at the cost of only a constant factor in its worst case time bound faster algorithms for a variety of combinatorial optimization problems follow from the result