problem method classification in optimization and control abstract there are many classifications in optimization and control continuous discrete integer problems convex or concave minimization steepest descent branch and bound path following space filling random search methods smooth or non smooth problems etc the aim of this short note is not to propose yet another classification but to clarify existing ambiguities and imprecisions in problem formulations and to emphasize certain fundamental distinctions in solution methods currently used

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

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

linear size optimal q ary constant weight codes and constant composition codes an optimal constant composition or constant weight code of weight w has linear size if and only if its distance d is at least 2w 1 when d 2w the determination of the exact size of such a constant composition or constant weight code is trivial but the case of d 2w 1 has been solved previously only for binary and ternary constant composition and constant weight codes and for some sporadic instances this paper provides a construction for quasicyclic optimal constant composition and constant weight codes of weight w and distance 2w 1 based on a new generalization of difference triangle sets as a result the sizes of optimal constant composition codes and optimal constant weight codes of weight w and distance 2w 1 are determined for all such codes of sufficiently large lengths this solves an open problem of etzion the sizes of optimal constant composition codes of weight w and distance 2w 1 are also determined for all w 6 except in two cases

estimates on the size of symbol weight codes the study of codes for powerline communications has garnered much interest over the past decade various types of codes such as permutation codes frequency permutation arrays and constant composition codes have been proposed over the years in this paper we study a type of code called bounded symbol weight codes which was first introduced by versfeld in 2005 and a related family of codes that we term constant symbol weight codes we provide new upper and lower bounds on the size of bounded symbol weight and constant symbol weight codes we also give direct and recursive constructions of codes for certain parameters

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

on a positive semidefinite relaxation of the cut polytope abstract we study the convex set l n defined by l n z x x xij a positive semidefinite n n matrix xii 1 for all i we describe several geometric properties of l n in particular we show that l n has 2n 1 vertices which are its rank one matrices corresponding to all bipartitions of the set 1 2 n our main motivation for investigating the convex set l n comes from combinatorial optimization namely from approximating the max cut problem an important property of l n is that due to the positive semidefinite constraints one can optimize over it in polynomial time on the other hand l n still inherits the difficult structure of the underlying combinatorial problem in particular it is np hard to decide whether the optimum of the problem min tr cx x ln is reached at a vertex this result follows from the complete characterization of the matrices c of the form c bbt for some vector b for which the optimum of the above program is reached at a vertex

connections between semidefinite relaxations of the max cut and stable set problems we describe links between a recently introduced semidefinite relaxation for the max cut problem and the well known semidefinite relaxation for the stable set problem underlying the lovasz s theta function it turns out that the connection between the convex bodies defining the semidefinite relaxations mimics the connection existing between the corresponding polyhedra we also show how the semidefinite relaxations can be combined with the classical linear relaxations in order to obtain tighter relaxations

an efficient maximization algorithm with implications in min max predictive control in this technical note an algorithm for binary quadratic programs defined by matrices with band structure is proposed it was shown in the article by t alamo d m de la pentildea d limon and e f camacho ldquoconstrained min max predictive control modifications of the objective function leading to polynomial complexity rdquo ieee tran autom control vol 50 pp 710 714 may 2005 that this class of problems arise in robust model predictive control when min max techniques are applied although binary quadratic problems belongs to a class of np complete problems the computational burden of the proposed maximization algorithm for band matrices is polynomial with the dimension of the optimization variable and exponential with the band size computational results and comparisons on several hundred test problems demonstrate the efficiency of the algorithm

two alternatives for the cubic algorithm abstract two alternatives are proved that allow application of the cubic algorithm for finding approximate solutions of the general non convex and non robust mathematical programming problem

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

a polyhedral approach to the single row facility layout problem the single row facility layout problem srflp is the np hard problem of arranging facilities on a line while minimizing a weighted sum of the distances between facility pairs in this paper a detailed polyhedral study of the srflp is performed and several huge classes of valid and facet inducing inequalities are derived some separation heuristics are presented along with a primal heuristic based on multi dimensional scaling finally a branch and cut algorithm is described and some encouraging computational results are given

a generalized upper bound and a multilevel construction for distance preserving mappings a new general upper bound is derived on the sum of the hamming distances between sequences when mapping from one set of sequences to another it is shown that a similar upper bound for mappings from binary sequences to permutation sequences is a special case of this upper bound and this is used to evaluate known mappings also new distance preserving mappings dpms from binary sequences to permutation sequences are presented based on a multilevel construction in addition to explicit distance conserving mappings distance increasing and distance reducing mappings are also presented several of the new dpms attain the upper bound

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

some remarks on exact linearization of a class of stochastic dynamical systems the higher order exact linearization of a class of scalar stochastic dynamic systems is presented in this note a suitable change of coordinates which transforms a nonlinear scalar system to a multidimensional linear one is proposed the cases of uncontrolled and controlled systems are considered

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

optimal ternary constant composition codes of weight four and distance five constant composition codes cccs are a generalization of constant weight codes and permutation codes the concept of group divisible codes an analog of group divisible designs in combinatorial design theory was first introduced by chee et al this new class of codes has been shown to be useful in recursive constructions of constant weight codes and constant composition codes in this paper we consider the problem of determining the maximal sizes of ternary constant composition codes of weight four and distance five using group divisible codes as the main tools we determine the exact values for these parameters the previously known results are those with code length no greater than 10

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

universal binary semidefinite relaxation for ml signal detection semidefinite relaxation sdr provides a computationally efficient polynomial time approximation of the maximum likelihood detector however most of the existing works mainly focus on particular signal constellations in this paper we propose a universal binary semidefinite relaxation scheme that can handle arbitrary signal constellations in polynomial time the proposed scheme first binarizes the original signal space to a linearly constrained binary space and then solves the detection problem through sdr colorblack a specialized dual barrier method is provided to solve the sdr more efficiently in addition we propose to apply on the fly decision feedback to further reduce the computational complexity and improve the detection performance the proposed binary sdr together with on the fly decision feedback scheme can provide comparable or better solutions compared to existing sdr methods specialized to specific constellations such as 16 qam and 8 psk in terms of computational complexity and symbol error rate furthermore the proposed scheme is universal and can solve any other constellations such as 12 qam 32 qam or m psk

efficient semidefinite branch and cut for map mrf inference we propose a branch and cut b c method for solving general map mrf inference problems the core of our method is a very efficient bounding procedure which combines scalable semidefinite programming sdp and a cutting plane method for seeking violated constraints in order to further speed up the computation several strategies have been exploited including model reduction warm start and removal of inactive constraints we analyze the performance of the proposed method under different settings and demonstrate that our method either outperforms or performs on par with state of the art approaches especially when the connectivities are dense or when the relative magnitudes of the unary costs are low we achieve the best reported results experiments show that the proposed algorithm achieves better approximation than the state of the art methods within a variety of time budgets on challenging non submodular map mrf inference problems

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

a family of optimal constant composition codes constant composition codes are a special class of constant weight codes with very strong constraints it is hard to construct optimal constant composition codes there are only a few classes of such optimal codes in the literature in this correspondence a family of optimal ternary constant composition codes is constructed from a class of newly discovered perfect nonlinear functions this class of codes is related to a new family of skew hadamard difference sets which are the only examples of such difference sets discovered in the last seventy years

an active set method for second order conic constrained quadratic programming we consider the minimization of a convex quadratic objective subject to second order cone constraints this problem generalizes the well studied bound constrained quadratic programming qp problem we propose a new two phase method in the first phase a projected gradient method is used to quickly identify the active set of cones and in the second phase newton s method is applied to rapidly converge given the subsystem of active cones computational experiments confirm that the conically constrained qp is solved more efficiently by our method than by a specialized conic optimization solver and more robustly than by general nonlinear programming solvers

inclusion functions and global optimization 11 inclusion functions combined with special subdivision strategies are an effective means of solving the global unconstrained optimization problem although these techniques were determined and numerically tested about ten years ago they are nearly unknown and scarcely used in order to make the role of inclusion functions and subdivision strategies more widespread and transparent we will discuss a related simplified basic algorithm it computes approximations of the global minimum and at the same time bounds the absolute approximation error we will show that the algorithm works and converges under more general assumptions than it has been known hitherto that is only appropriate inclusion functions are expected to exist the number of minimal points finite or infinite is not of importance lipschitz conditions or continuity are not assumed as shown in the appendix the required inclusion functions can be constructed and programmed without difficulty in a natural way using interval analysis

robust convex optimization we study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u yet the constraints must hold for all possible values of the data from u the ensuing optimization problem is called robust optimization in this paper we lay the foundation of robust convex optimization in the main part of the paper we show that if u is an ellipsoidal uncertainty set then for some of the most important generic convex optimization problems linear programming quadratically constrained programming semidefinite programming and others the corresponding robust convex program is either exactly or approximately a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods

performance of simulated annealing based heuristic for the unconstrained binary quadratic programming problem abstract the unconstrained binary quadratic programming problem bqp is known to be np hard and has many practical applications this paper presents a simulated annealing sa based heuristic for the bqp the new sa heuristic for the bqp is based on a simple 1 opt local search heuristic and designed with a simple cooling schedule but the multiple annealing processes are adopted to show practical performances of the sa we test on publicly available benchmark instances of large size ranging from 500 to 2500 variables and compare them with other heuristics such as multi start local search the previous sa tabu search and genetic algorithm incorporating the 1 opt local search computational results indicate that our sa leads to high quality solutions with short times and is more effective than the competitors particularly for the largest benchmark set furthermore the values of new best known solutions found by the sa for several large instances are also reported

nonpolyhedral relaxations of graph bisection problems we study the problem of finding the minimum bisection of a graph into two parts of prescribed sizes we formulate two lower bounds on the problem by relaxing node and edge incidence vectors of cu

applications of cut polyhedra ii abstract in this paper and in its continuation part ii this issue we group within a unified framework many applications of the following polyhedra cut boolean quadric hypermetric and metric polyhedra we treat in particular the following applications l1 and l1 metrics in functional analysis the max cut problem the boole problem and multicommodity flow problems in combinatorial optimization lattice holes in geometry of numbers density matrices of many fermions systems in quantum mechanics we present some other applications in probability theory statistical data analysis and design theory in this first part after introducing the main definitions and operations for cut polyhedra we describe the connections with l1 metrics and with other metric properties and we consider in particular the applications to some classes of metrics arising from graphs normed spaces and lattices

robust discrete optimization and network flows we propose an approach to address data uncertainty for discrete optimization and network flow problems that allows controlling the degree of conservatism of the solution and is computationally tractable both practically and theoretically in particular when both the cost coefficients and the data in the constraints of an integer programming problem are subject to uncertainty we propose a robust integer programming problem of moderately larger size that allows controlling the degree of conservatism of the solution in terms of probabilistic bounds on constraint violation when only the cost coefficients are subject to uncertainty and the problem is a 0 1 discrete optimization problem on n variables then we solve the robust counterpart by solving at most n 1 instances of the original problem thus the robust counterpart of a polynomially solvable 0 1 discrete optimization problem remains polynomially solvable in particular robust matching spanning tree shortest path matroid intersection etc are polynomially solvable we also show that the robust counterpart of an np hard approximable 0 1 discrete optimization problem remains approximable finally we propose an algorithm for robust network flows that solves the robust counterpart by solving a polynomial number of nominal minimum cost flow problems in a modified network

quasi maximum likelihood multiuser detection using semi definite relaxation with application to synchronous cdma the maximum likelihood ml multiuser detector is well known to exhibit better bit error rate ber performance than many other multiuser detectors unfortunately ml detection mld is a nondeterministic polynomial time hard np hard problem for which there is no known algorithm that can find the optimal solution with polynomial time complexity in the number of users in this paper a polynomial time approximation method called semi definite sd relaxation is applied to the mld problem with antipodal data transmission sd relaxation is an accurate approximation method for certain np hard problems the sd relaxation ml sdr ml detector is efficient in that its complexity is of the order of k3 5 where k is the number of users we illustrate the potential of the sdr ml detector by showing that some existing detectors such as the decorrelator and the linear minimum mean square error detector can be interpreted as degenerate forms of the sdr ml detector simulation results indicate that the ber performance of the sdr ml detector is better than that of these existing detectors and is close to that of the true ml detector even when the cross correlations between users are strong or the near far effect is significant

some old traditions in mathematics and in mathematical education abstract continuing the discussion by azbelev about the harmful influence of some classical traditions on the study of differential equations 1 this note presents further instances of old traditions and of their impact on the development of certain areas of mathematics and its applications

constructing coset codes with optimal same symbol weight for detecting narrowband interference in m fsk systems narrowband interference can cause undetected errors when m fsk data is encoded with an algebraic code containing the all e codewords this is due to the fact that the narrowband interferer will cause the output of the m fsk demodulator to correspond to one of the all e codewords one possible solution is to use a coset code of a code containing the repetition code the choice of the coset leader should be such that the resulting coset code has minimum same symbol weight we give a general construction for generating coset codes with minimum same symbol weight and present results where an optimal coset code for an n k reed solomon code is applied in an m fsk environment with narrowband interference from the results it is evident that the optimal coset codes outperform linear codes when narrowband interference is present

some remarks about moment controllability for linear stochastic systems the moment controllability of linear systems containing white multiplicative noise processes is considered we introduce the definition of p th moment controllability and we present a technique for obtaining sufficient conditions for this controllability an example is given to illustrate the technique

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

cuts for mixed 0 1 conic programming in this we paper we study techniques for generating valid convex constraints for mixed 0 1 conic programs we show that many of the techniques developed for generating linear cuts for mixed 0 1 linear programs such as the gomory cuts the lift and project cuts and cuts from other hierarchies of tighter relaxations extend in a straightforward manner to mixed 0 1 conic programs we also show that simple extensions of these techniques lead to methods for generating convex quadratic cuts gomory cuts for mixed 0 1 conic programs have interesting implications for comparing the semidefinite programming and the linear programming relaxations of combinatorial optimization problems e g we show that all the subtour elimination inequalities for the traveling salesman problem are rank 1 gomory cuts with respect to a single semidefinite constraint we also include results from our preliminary computational experiments with these cuts

on constant composition codes over z sub q a constant composition code is a special constant weight code under the restriction that each symbol should appear a given number of times in each codeword in this correspondence we give a lower bound for the maximum size of the q ary constant composition codes with minimum distance at least 3 this bound is asymptotically optimal and generalizes the graham sloane bound for binary constant weight codes in addition three construction methods of constant composition codes are presented and a number of optimum constant composition codes are obtained by using these constructions

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

combinatorial constructions of optimal constant composition codes constant composition codes cccs are a special class of constant weight codes they include permutation codes as a subclass in this correspondence a link between cccs and generalized double resolvable packing designs is developed and used to construct several infinite series of optimal cccs

certifiably optimal sparse inverse covariance estimation we consider the maximum likelihood estimation of sparse inverse covariance matrices we demonstrate that current heuristic approaches primarily encourage robustness instead of the desired sparsity we give a novel approach that solves the cardinality constrained likelihood problem to certifiable optimality the approach uses techniques from mixed integer optimization and convex optimization and provides a high quality solution with a guarantee on its suboptimality even if the algorithm is terminated early using a variety of synthetic and real datasets we demonstrate that our approach can solve problems where the dimension of the inverse covariance matrix is up to 1000 s we also demonstrate that our approach produces significantly sparser solutions than glasso and other popular learning procedures makes less false discoveries while still maintaining state of the art accuracy

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

nonlinear equations and optimization abstract interval analysis has led to improved numerical algorithms both for the solution of nonlinear equations and for nonlinear optimization in fact interval analysis has made possible algorithms for solving a problem often predicted to be numerically insoluble the nonlinear global optimization problem in this paper we survey interval methods for solving nonlinear equations and optimization

semidefinite relaxations of robust binary least squares under ellipsoidal uncertainty sets the problem of finding the least squares solution s to a system of equations hs y is considered when s is a vector of binary variables and the coefficient matrix h is unknown but of bounded uncertainty similar to previous approaches to robust binary least squares we explore the potential of a min max design with the aim to provide solutions that are less sensitive to the uncertainty in h we concentrate on the important case of ellipsoidal uncertainty i e the matrix h is assumed to be a deterministic unknown quantity which lies in a given uncertainty ellipsoid the resulting problem is np hard yet amenable to convex approximation techniques starting from a convenient reformulation of the original problem we propose an approximation algorithm based on semidefinite relaxation that explicitly accounts for the ellipsoidal uncertainty in the coefficient matrix next we show that it is possible to construct a tighter relaxation by suitably changing the description of the feasible region of the problem and formulate an approximation algorithm that performs better in practice interestingly both relaxations are derived as lagrange bidual problems corresponding to the two equivalent problem reformulations the strength of the proposed tightened relaxation is demonstrated by pertinent simulations

importance of symbol equity in coded modulation for power line communications the use of multiple frequency shift keying modulation with permutation codes addresses the problem of permanent narrowband noise disturbance in a power line communications system in this paper we extend this coded modulation scheme based on permutation codes to general codes and introduce an additional new parameter that more precisely captures a code s performance against permanent narrowband noise as a result we define a new class of codes namely equitable symbol weight codes which are optimal with respect to this measure

detection of stochastic processes this paper reviews two streams of development from the 1940 s to the present in signal detection theory the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance this treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous time stochastic processes the mathematics and intuition behind such developments as the matched filter the rake receiver the estimator correlator maximum likelihood sequence detectors multiuser detectors sequential probability ratio tests and cumulative sum quickest detectors are described

cut polytopes boolean quadratic polytopes and nonnegative quadratic pseudo boolean functions in this paper we present a class of valid inequalities as well as a class of facets for the cut polytope of the complete graph it is shown that many of the known classes of valid inequalities e g triangle hypermetric and cycle inequalities belong to this class by specializing some of the parameters large classes of facets can be defined it is shown that each of these classes contains at least n 3n 3 facets where n 10 denotes the number of vertices and that the corresponding separation problems are polynomially solvable these results are based on a one to one correspondence established between the set of valid inequalities facets for the cut polytope of kn 1 and the set of nonnegative extremal quadratic pseudo boolean functions in n variables

laplacian eigenvalues and the maximum cut problem we introduce and study an eigenvalue upper bound g on the maximum cut mc g of a weighted graph the function g has several interesting properties that resemble the behaviour of mc g the following results are presented we show that is subadditive with respect to amalgam and additive with respect to disjoint sum and 1 sum we prove that g is never worse that 1 131 mc g for a planar or more generally a weakly bipartite graph with nonnegative edge weights we give a dual characterization of g and show that g is computable in polynomial time with an arbitrary precision

algebraic constructions of constant composition codes constant composition codes are a special class of constant weight codes they include permutation codes as a subclass in this correspondence two classes of optimal constant composition codes are constructed both constructions employ perfect nonlinear functions but they are different

maximum likelihood sequence estimators a geometric view communication issues are described in terms of macro operations between the data and the observation spaces the problem of recovering the data is related to the inversion of an operator the channel mapping for this reason results available in linear algebra and functional analysis are applicable traditional concepts in communications are identified with these operations an approach to the maximum likelihood sequence estimator based on a sufficient statistic derived from these concepts is proposed intersymbol interference is removed by linear equalization and a viterbi like dynamic programming algorithm takes into account the correlated noise in the metric evaluation the performance of suboptimal receivers obtained by means of metric simplification is analyzed

controllability of stochastic linear systems in the paper necessary and sufficient conditions for various types of stochastic controllability of the linear stochastic system of the form d x ax d t bu d t c d w r x 0 x 0 are given some possible extensions are indicated as well

the pbd closure of constant composition codes we show an interesting pairwise balanced design pbd closure result for the set of lengths of constant composition codes whose distance and size meet certain conditions a consequence of this pbd closure result is that the size of optimal constant composition codes can be determined for infinite families of parameter sets from just a single example of an optimal code as an application the sizes of several infinite families of optimal constant composition codes are derived in particular the problem of determining the size of optimal constant composition codes having distance four and weight three is solved for all lengths sufficiently large this problem was previously unresolved for odd lengths except for lengths seven and eleven

global optimization to prescribed accuracy abstract programmable methods are outlined for rigorous global optimization to prescribed accuracy with references to enough detail to enable the implementation of the techniques on any computer some directions for future research are indicated

semidefinite relaxation based multiuser detection for m ary psk multiuser systems because of the powerful symbol error performance of multiuser maximum likelihood ml detection recently there has been much interest in seeking effective ways of approximating multiuser ml detection mld with affordable computational costs it has been illustrated that for the synchronous code division multiple access cdma scenario the so called semidefinite relaxation sdr algorithm can accurately and efficiently approximate multiuser mld this sdr mld algorithm however can only handle binary and quadratic phase shift keying psk symbol constellations in this sequel we propose an extended sdr algorithm for mld with m ary psk mpsk constellations for the synchronous cdma scenario the proposed sdr algorithm provides an attractive polynomial time complexity order of k sup 3 5 where k is the number of users simulation results indicate that the proposed detector provides improved symbol error performance compared with several commonly used multiuser detectors

on the complexity of a class of combinatorial optimization problems with uncertainty we consider a robust minmax regret version of the problem of selecting p elements of minimum total weight out of a set of m elements with uncertainty in weights of the elements we present a polynomial algorithm with the order of complexity o min p m p 2m for the case where uncertainty is represented by means of interval estimates for the weights we show that the problem is np hard in the case of an arbitrary finite set of possible scenarios even if there are only two possible scenarios this is the first known example of a robust combinatorial optimization problem that is np hard in the case of scenario represented uncertainty but is polynomially solvable in the case of the interval representation of uncertainty

the diversity order of the semidefinite relaxation detector in this paper we consider the detection of binary antipodal signals transmitted in a spatially multiplexed fashion over a fading multiple input multiple output mimo channel and where the detection is done by means of semidefinite relaxation sdr the sdr detector is an attractive alternative to maximum likelihood ml detection since the complexity is polynomial rather than exponential assuming that the channel matrix is drawn with independent identically distributed i i d real valued gaussian entries we study the receiver diversity and prove that the sdr detector achieves the maximum possible diversity thus the error probability of the receiver tends to zero at the same rate as the optimal ml receiver in the high signal to noise ratio snr limit this significantly strengthens previous performance guarantees available for the semidefinite relaxation detector additionally it proves that full diversity detection is also possible in certain scenarios when using a noncombinatorial receiver structure