cut generation through binarization for a mixed integer linear program where all integer variables are bounded we study a reformulation introduced by roy that maps general integer variables to a collection of binary variables we study theoretical properties and empirical strength of rank 2 simple split cuts of the reformulation we show that for a pure integer problem with two integer variables these cuts are sufficient to obtain the integer hull of the problem but that this does not generalize to problems in higher dimensions we also give an algorithm to compute an approximation of the rank 2 simple split cut closure we report empirical results on 22 benchmark instances showing that the bounds obtained compare favorably with those obtained with other approximate methods to compute the split closure or lattice free cut closure it gives a better bound than the split closure on 6 instances while it is weaker on 9 instances for an average gap closed 3 8 smaller than the one for the split closure

on yau s problem of evolving one curve to another convex case abstract a revised yau s curvature difference flow is considered to deform one convex curve x 0 to another one x it is proved that this flow exists globally on time interval 0 and the evolving curve preserving its convexity and bounded area a converges to a fixed limiting curve x congruent to a a x as time tends to infinity where a is the area bounded by the target curve x

on the exact solution of a facility layout problem we consider the layout problem of arranging a number of departments on a line this problem is known as single row facility layout the problem is very difficult to be solved in fact it has as a particular case the linear ordering problem which is strongly np hard in this paper a new mixed integer linear programming model is proposed for the problem theoretical arguments as well as computational results are given which demonstrate the efficiency of the new model relatively to previous mixed integer linear programming models proposed for the problem

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

lower bound for the number of iterations in semidefinite hierarchies for the cut polytope hierarchies of semidefinite relaxations for 0 1 polytopes have been constructed by lasserre 2001a and by lovaisz and schrijver 1991 the cut polytope of a graph onn nodes can be expressed as a projection of such a semidefinite relaxation after at mostn steps we show that n 2 iterations are needed for finding the cut polytope of the complete graphk n

on a length preserving inverse curvature flow of convex closed plane curves abstract this paper deals with a 1 type length preserving nonlocal flow of convex closed plane curves for all 0 under this flow the convexity of the evolving curve is preserved for a global flow it is shown that the evolving curve converges smoothly to a circle as t some numerical blow up examples and a sufficient condition leading to the global existence of the flow are also constructed

convex relaxations of non convex mixed integer quadratically constrained programs extended formulations this paper addresses the problem of generating strong convex relaxations of mixed integer quadratically constrained programming miqcp problems miqcp problems are very difficult because they combine two kinds of non convexities integer variables and non convex quadratic constraints to produce strong relaxations of miqcp problems we use techniques from disjunctive programming and the lift and project methodology in particular we propose new methods for generating valid inequalities from the equation y x x t we use the non convex constraint y x x t preccurlyeq 0 to derive disjunctions of two types the first ones are directly derived from the eigenvectors of the matrix y x x t with positive eigenvalues the second type of disjunctions are obtained by combining several eigenvectors in order to minimize the width of the disjunction we also use the convex sdp constraint y x x t succcurlyeq 0 to derive convex quadratic cuts and we combine both approaches in a cutting plane algorithm we present computational results to illustrate our findings

exponential lower bounds for polytopes in combinatorial optimization we solve a 20 year old problem posed by yannakakis and prove that no polynomial size linear program lp exists whose associated polytope projects to the traveling salesman polytope even if the lp is not required to be symmetric moreover we prove that this holds also for the cut polytope and the stable set polytope these results were discovered through a new connection that we make between one way quantum communication protocols and semidefinite programming reformulations of lps

computing deep facet defining disjunctive cuts for mixed integer programming the problem of separation is to find an affine hyperplane or cut that lies between the origin o and a given closed convex set q in a euclidean space we study cuts which are deep in a well defined geometrical sense and facet defining the cases when the deepest cut is decomposable as a combination of facet defining cuts are characterized using the reverse polar set when q is a disjunctive polyhedron a description of the reverse polar linked to the so called cut generating linear program of lift and project techniques is given a successive projections algorithm onto the reverse polar is proposed that computes the decomposition of the deepest cut into facet defining cuts illustrative numerical experiments show how these cuts compare with the deepest cut and with the most violated cut

experimental analysis of simulated annealing based algorithms for the layout problem abstract in this paper results from an experimental analysis involving the 2 way and 3 way exchange algorithms a modified penalty algorithm the simulated annealing algorithm and a hybrid simulated annealing algorithm are presented the hybrid simulated annealing algorithm uses the modified penalty algorithm to generate an initial solution and then improves it using simulated annealing it is tested on single row layout problems with facilities of unequal area and multi row layout problems with facilities of equal area the algorithm produced solutions better than those previously reported in the literature for two of the larger single row problems and five multi row layout problems for all the other single row problems and eight of ten multi row layout test problems it produced the best known solutions the hybrid simulated annealing algorithm appears to produce better quality solutions than the simulated annealing and tabu navigation algorithms but requires more computation time than simulated annealing

refined factorizations of solvable potentials a generalization of the factorization technique is shown to be a powerful algebraic tool to discover further properties of a class of integrable systems in quantum mechanics the method is applied in the study of radial oscillator morse and coulomb potentials to obtain a wide set of raising and lowering operators and to show clearly the connection that links these systems

a cutting surface method for uncertain linear programs with polyhedral stochastic dominance constraints in this paper we study linear optimization problems with a newly introduced concept of multidimensional polyhedral linear second order stochastic dominance constraints by using the polyhedral properties of this dominance condition we present a cutting surface algorithm and show its finite convergence the cut generation problem is a difference of convex functions dc optimization problem we exploit the polyhedral structure of this problem to present a novel branch and cut algorithm that incorporates concepts from concave minimization and binary integer programming a linear programming problem is formulated for generating concavity cuts in our case where the polyhedra are unbounded we also present duality results for this problem relating the dual multipliers to utility functions without the need to impose constraint qualifications which again is possible because of the polyhedral nature of the problem numerical examples are presented showing the nature of solutions of our model a corrected pdf has been appended to the original

stochastic programming with integer variables including integer variables into traditional stochastic linear programs has considerable implications for structural analysis and algorithm design starting from mean risk approaches with different risk measures we identify corresponding two and multi stage stochastic integer programs that are large scale block structured mixed integer linear programs if the underlying probability distributions are discrete we highlight the role of mixed integer value functions for structure and stability of stochastic integer programs when applied to the block structures in stochastic integer programming well known algorithmic principles such as branch and bound lagrangian relaxation or cutting plane methods open up new directions of research we review existing results in the field and indicate departure points for their extension

facets of the linear ordering polytope letd n be the complete digraph onn nodes and letp lo denote the convex hull of all incidence vectors of arc sets of linear orderings of the nodes ofd n i e these are exactly the acyclic tournaments ofd n we show that various classes of inequalities define facets ofp lo e g the 3 dicycle inequalities the simplek fence inequalities and various mobius ladder inequalities and we discuss the use of these inequalities in cutting plane approaches to the triangulation problem of input output matrices i e the solution of permutation resp linear ordering problems

scattering potentials with ls terms from first order casimir operators using a first order casimir operator calculated in a non standard realization for the so 3 1 algebra we obtain a one dimensional scattering problem with ls type interaction terms it is shown that for this realization the square of this operator can be expressed in terms of the usual quadratic casimir due to this constraint the scattering states are completely specified by restricting the possible set of eigenvalues accordingly the results show that the use of extra casimir operators can provide additional insight into the group theoretical structure of the scattering problem a generalization for the so 2n 1 1 n 2 case is also given the underlying supersymmetry of the resulting schrodinger equations is pointed out the supersymmetric charge operators are related to our first order casimir operators

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

on solving discrete two stage stochastic programs having mixed integer first and second stage variables in this paper we propose a decomposition based branch and bound dbab algorithm for solving two stage stochastic programs having mixed integer first and second stage variables a modified benders decomposition method is developed where the benders subproblems define lower bounding second stage value functions of the first stage variables that are derived by constructing a certain partial convex hull representation of the two stage solution space this partial convex hull is sequentially generated using a convexification scheme such as the reformulation linearization technique rlt or lift and project process which yields valid inequalities that are reusable in the subsequent subproblems by updating the values of the first stage variables a branch and bound algorithm is designed based on a hyperrectangular partitioning process using the established property that any resulting lower bounding benders master problem defined over a hyperrectangle yields the same objective value as the original stochastic program over that region if the first stage variable solution is an extreme point of the defining hyperrectangle or the second stage solution satisfies the binary restrictions we prove that this algorithm converges to a global optimal solution some numerical examples and computational results are presented to demonstrate the efficacy of this approach

extended formulations for packing and partitioning orbitopes we give compact extended formulations for the packing and partitioning orbitopes with respect to the full symmetric group described and analyzed in kaibel and pfetsch kaibel v m e pfetsch 2008 packing and partitioning orbitopes math programming ser a114 1 1 36 these polytopes are the convex hulls of all 0 1 matrices with lexicographically sorted columns and at most respectively exactly one 1 entry per row they are important objects for symmetry reduction in certain integer programs using the extended formulations we also derive a rather simple proof of the fact established in the paper mentioned above that basically shifted column inequalities suffice to describe those orbitopes linearly

a lift and project cutting plane algorithm for mixed 0 1 programs we propose a cutting plane algorithm for mixed 0 1 programs based on a family of polyhedra which strengthen the usual lp relaxation we show how to generate a facet of a polyhedron in this family which is most violated by the current fractional point this cut is found through the solution of a linear program that has about twice the size of the usual lp relaxation a lifting step is used to reduce the size of the lp s needed to generate the cuts an additional strengthening step suggested by balas and jeroslow is then applied we report our computational experience with a preliminary version of the algorithm this approach is related to the work of balas on disjunctive programming the matrix cone relaxations of lovasz and schrijver and the hierarchy of relaxations of sherali and adams

a disjunctive cutting plane procedure for general mixed integer linear programs in this paper we develop a cutting plane algorithm for solving mixed integer linear programs with general integer variables a novel feature of the algorithm is that it generates inequalities at all optimal vertices of the lp relaxation at each iteration the cutting planes generated in the procedure are found by considering a natural generalization of the 0 1 disjunction used by balas ceria and cornuejols in the context of solving binary mixed integer linear programs 3 4

strong formulations for mixed integer programs valid inequalities and extended formulations we examine progress over the last fifteen years in finding strong valid inequalities and tight extended formulations for simple mixed integer sets lying both on the easy and hard sides of the complexity frontier most progress has been made in studying sets arising from knapsack and single node flow sets and a variety of sets motivated by different lot sizing models we conclude by citing briefly some of the more intriguing new avenues of research

combinatorial optimization current successes and directions for the future our ability to solve large important combinatorial optimization problems has improved dramatically in the past decade the availability of reliable software extremely fast and inexpensive hardware and high level languages that make the modeling of complex problems much faster have led to a much greater demand for optimization tools this paper highlights the major breakthroughs and then describes some very exciting future opportunities previously large research projects required major data collection efforts expensive mainframes and substantial analyst manpower now we can solve much larger problems on personal computers much of the necessary data is routinely collected and tools exist to speed up both the modeling and the post optimality analysis with the information technology revolution taking place currently we now have the opportunity to have our tools embedded into supply chain systems that determine production and distribution schedules process design and location allocation decisions these tools can be used industry wide with only minor modifications being done by each user

cones of matrices and set functions and 0 1 optimization it has been recognized recently that to represent a polyhedron as the projection of a higher dimensional but simpler polyhedron is a powerful tool in polyhedral combinatorics a general method is developed to construct higher dimensional polyhedra or in some cases convex sets whose projection approximates the convex hull of 0 1 valued solutions of a system of linear inequalities an important feature of these approximations is that one can optimize any linear objective function over them in polynomial time in the special case of the vertex packing polytope a sequence of systems of inequalities is obtained such that the first system already includes clique odd hole odd antihole wheel and orthogonality constraints in particular for perfect and many other graphs this first system gives the vertex packing polytope for various classes of graphs including t perfect graphs it follows that the stable set polytope is the projection of a polytope with a polynomial number of facets an extension o

on the one dimensional space allocation problem the one dimensional space allocation problem odsap arises when locating rooms along a corridor when setting books on a shelf when allocating information items among the cylinders of a magnetic disk or when storing products in certain warehouses the rooms objects to be located have a known length or width and for each pair of rooms there is a given number of trips between them the problem is to find a sequencing of the rooms which minimizes the total traveled distance this paper deals first with two particular cases in the rooted tree case previous results obtained by adolphson and t c hu for the linear ordering problem are extended and provide efficient solution methods in addition it is shown that most of the assumptions made by adolphson and hu are necessary since relaxing any of them leads to an np complete problem in the case of independent destinations solved by bergmans and pratt when all lengths are equal a unimodality property is shown for an optimum solution but this is not sufficient to lead to a good algorithm and the problem is shown to be np complete for the general problem an exact algorithm using dynamic programming is described and computationally tested

single row facility layout problem using a permutation based genetic algorithm in this paper a permutation based genetic algorithm ga is applied to the np hard problem of arranging a number of facilities on a line with minimum cost known as the single row facility layout problem srflp the ga individuals are obtained by using some rule based as well as random permutations of the facilities which are then improved towards the optimum by means of specially designed crossover and mutation operators such schemes led the ga to handle the srflp as an unconstrained optimization problem in the computational experiments carried out with large size instances of sizes from 60 to 80 available in the literature the proposed ga improved several previously known best solutions

hybridizing variable neighborhood search with ant colony optimization for solving the single row facility layout problem abstract in this paper a hybrid algorithm based on variable neighborhood search and ant colony optimization is proposed to solve the single row facility layout problem in the proposed algorithm three neighborhood structures are utilized to enhance the exploitation ability meanwhile new gain techniques are developed to reduce the mathematical calculations of the objective function values furthermore ant colony optimization as the shaking step is used to avoid being stuck at the local optima in addition a novel pheromone updating rule has been proposed based on both the best and worst solutions of the ants a reverse criterion based on edit distance measure is applied to help ants to converge to the best solution and reduce the solution space finally numerical simulation is carried out based on the benchmark instances and the comparisons with some existing algorithms demonstrate the effectiveness of the proposed algorithm

mixed 0 1 programming by lift and project in a branch and cut framework we investigate the computational issues that need to be addressed when incorporating general cutting planes for mixed 0 1 programs into a branch and cut framework the cuts we use are of the lift and project variety some of the issues addressed have a theoretical answer but others are of an experimental nature and are settled by comparing alternatives on a set of test problems the resulting code is a robust solver for mixed 0 1 programs we compare it with several existing codes on a wide range of test problems it performs as well as or better than some of the best currently available mixed integer programming codes

multiphase thermomechanics with interfacial structure 2 evolution of an isothermal interface paper 1 1988 g 1 of this series began an investigation whose goal is a thermomechanics of two phase continua based on gibbs s notion of a sharp phase interface endowed with thermomechanical structure in that paper a balance law balance of capillary forces was introduced and then applied in conjunction with suitable statements of the first two laws of thermodynamics the chief results are thermodynamic restrictions on constitutive equations exact and approximate free boundary conditions at the interface and a hierarchy of free boundary problems the simplest versions of these problems the mullins sekerka problems are essentially the classical stefan problem with the free boundary condition u 0 for the temperature replaced by the condition u h k where k is the curvature of the free boundary and h 0 is a material constant this dependence on curvature renders the problem difficult and apart from numerical studies involving linearization stability there are almost no supporting theoretical results

convex hull representation of the deterministic bipartite network interdiction problem we consider a version of the stochastic network interdiction problem modeled by morton et al iie trans 39 3 14 2007 in which an interdictor attempts to minimize a potential smuggler s chance of evasion via discrete deployment of sensors on arcs in a bipartite network the smuggler reacts to sensor deployments by solving a maximum reliability path problem on the resulting network in this paper we develop the minimal convex hull representation for the polytope linking the interdictor s decision variables with the smuggler s for the case in which the smuggler s origin and destination are known and interdictions are cardinality constrained in the process we propose an exponential class of easily separable inequalities that generalize all of those developed so far for the bipartite version of this problem we show how these cuts may be employed in a cutting plane fashion when solving the more difficult problem in which the smuggler s origin and destination are stochastic and argue that some instances of the stochastic model have facets corresponding to the solution of np hard problems our computational results show that the cutting planes developed in this paper may strengthen the linear programming relaxation of the stochastic model by as much as 25

anisotropic flows for convex plane curves where v and k are respectively the normal velocity and curvature of the interface equation 1 is sometimes called the curve shortening problem because it is the negative l2 gradient flow of the length of the interface by drawing pictures one can be easily convinced that a simple closed curve stays simple and smooth along 1 and shrinks to a point in finite time with the limiting shape of a circle however a mathematical treatment of 1 turned out to be rather delicate in fact a rigorous study did not exist until the early 1980s when differential geometers considered 1 as a tool in the search for simple closed geodesics on surfaces it was also regarded as a model case for more general curvature flows which are believed to be important in the topological classification of low dimensional manifolds as a first attempt gage 10 proved that the isoperimetric ratio decreases along convex curves then in gage and hamilton 12 it was shown that a convex curve stays convex and shrinks to a point in finite time moreover if one normalizes the flow by dilating it so that the enclosing area is constant the normalized flow converges smoothly to a circle finally grayson 14 completed this line of investigation by showing that a simple curve evolves into a convex one before shrinks to a point for an alternative approach to this result one may consult hamilton 18 recently mullins s theory was generalized by gurtin 15 16 and by angenent and gurtin 4 5 see also the monograph of gurtin 17 to include anisotropy and the possibility of a difference in bulk energies between phases anisotropy is indispensable in dealing with crystalline materials for perfect conductors the temperatures in both phases are constant the equation becomes

factorization of spin dependent hamiltonians we generalize the formalism of the factorization method by introducing spin degrees of freedom in addition to local potential terms we compare this construction with conventional factorization techniques of non relativistic hamiltonians and the formalism of supersymmetric quantum mechanics the characteristic isospectrality of the hamiltonians h1 qr and h2 rq is maintained in our more general framework as illustrative examples we consider two exactly solvable models related to the harmonic oscillator and the coulomb problems and some quasi exactly solvable problems in all three cases the zero energy ground state of h1 is found to be infinitely degenerate further possible generalizations of our approach are also outlined

lower bounds for nonlinear assignment problems using many body interactions abstract this paper concerns lower bounding techniques for the general adic assignment problem the nonlinear objective function is linearized by the introduction of additional variables and constraints thus yielding a mixed integer linear programming formulation of the problem the concept of many body interactions is introduced to strengthen this formulation and incorporated in a modified formulation obtained by lifting the original representation to a higher dimensional space this process involves two steps i addition of new variables and constraints and ii incorporation of the new variables in the objective function if this lifting process is repeated times on an adic assignment problem along with the incorporation of higher order interactions it results in the mixed integer formulation of an equivalent adic assignment problem the incorporation of many body interactions in the higher dimensional formulation improves its degeneracy properties and is also critical to the derivation of decomposition methods for the solution of these large scale mathematical programs in the higher dimensional space it is shown that a lower bound to the optimal solution of the corresponding linear programming relaxation can be obtained by dualizing a subset of constraints in this formulation and solving o n 2 1 linear assignment problems whose coefficients depend on the dual values moreover it is proved that the optimal solution to the lp relaxation is obtained if we use the optimal duals for the solution of the linear assignment problems this concept of many body interactions could be applied in designing algorithms for the solution of formulations obtained by lifting general milp s we illustrate all these concepts on the quadratic assignment problems with these decomposition bounds we have found the provably optimal solutions of two unsolved qap s of size 32 and have also improved upon existing lower bounds for other qap s

projected chvatal gomory cuts for mixed integer linear programs recent experiments by fischetti and lodi show that the first chvatal closure of a pure integer linear program ilp often gives a surprisingly tight approximation of the integer hull they optimize over the first chvatal closure by modeling the chvatal gomory cg separation problem as a mixed integer linear program milp which is then solved by a general purpose milp solver unfortunately this approach does not extend immediately to the gomory mixed integer gmi closure of an milp since the gmi separation problem involves the solution of a nonlinear mixed integer program or a parametric milp in this paper we introduce a projected version of the cg cuts and study their practical effectiveness for milp problems the idea is to project first the linear programming relaxation of the milp at hand onto the space of the integer variables and then to derive chvatal gomory cuts for the projected polyhedron though theoretically dominated by gmi cuts projected cg cuts have the advantage of producing a separation model very similar to the one introduced by fischetti and lodi which can typically be solved in a reasonable amount of computing time

solvable potentials associated with su 1 1 algebras a systematic study we consider a specific differential realization of the su 1 1 algebra and use it to explore such algebraic structures associated with shape invariant potentials our approach combines elements of various methods of solving the schrodinger equation such as supersymmetric quantum mechanics or the factorization method algebraic techniques and special function theory in fact it amounts to reformulating transformations mapping the schrodinger equation into the differential equation of orthogonal polynomials in group theoretical terms our systematic study recovers a number of earlier results in a natural unified way and also leads to new findings the procedure presented here implicitly contains a similar treatment of the compact su 2 algebra as well possible generalizations of this approach involving different realizations of the su 1 1 algebra other algebraic structures and larger classes of potentials are also outlined

on a simple maximum principle technique applied to equations on the circle abstract for a class of general quasilinear equations on s 1 we show that by a very simple maximum principle technique as long as the solution stays finite all of its derivatives also remain finite some specific examples are given under suitable assumptions we also derive exponential decay of the derivatives of the solution

tabu search for the single row facility layout problem using exhaustive 2 opt and insertion neighborhoods abstract the single row facility layout problem srflp is the problem of arranging facilities with given lengths on a line while minimizing the weighted sum of the distances between all pairs of facilities the problem is np hard in this paper we present two tabu search implementations one involving an exhaustive search of the 2 opt neighborhood and the other involving an exhaustive search of the insertion neighborhood we also present techniques to significantly speed up the search of the two neighborhoods our computational experiments show that the speed up techniques are effective and our tabu search implementations are competitive our tabu search implementations improved previously known best solutions for 23 out of the 43 large sized srflp benchmark instances

solving mixed integer programming problems using automatic reformulation in this paper we describe computational experience in solving mixed 0 1 programming problems using strong valid inequalities as cutting planes in particular we report on the solution to optimality of 18 medium to large size problems including production planning problems with setup costs and capacity constraints multilevel distribution planning problems drainage and heating system design problems and electricity generator scheduling problems the solution approach uses the theory of strong valid inequalities that we developed in a series of earlier papers here we report specifically on the implementation of an experimental system mpsarx which consists of the sciconic mathematical programming system and an automatic reformulation executor arx that use this theory and on the results obtained with this system

efficient models for the facility layout problem abstract in this paper two new models of the facility layout problem are presented linear continuous with absolute values in the objective function and constraints and linear mixed integer the linear mixed integer models have lesser number of integer variables than any other existing formulation for the facility layout problem while most other linear mixed integer models available in the literature have been obtained through a linearization of the quadratic assignment problem the ones presented in this paper are not the continuous models have an even more compact form an advantage of the formulations presented in this paper is that the location of sites need not be known a priori more importantly two of the formulations model the layout problem with facilities of unequal area solving the models presented with an unconstrained optimization algorithm yields good quality suboptimal solutions in a relatively low computation time the continuous models appear to be more useful for solving the facility layout problem than other models published in the literature

sequential convexification in reverse convex and disjunctive programming this paper is about a property of certain combinatorial structures called sequential convexifiability shown by balas 1974 1979 to hold for facial disjunctive programs sequential convexifiability means that the convex hull of a nonconvex set defined by a collection of constraints can be generated by imposing the constraints one by one sequentially and generating each time the convex hull of the resulting set here we extend the class of problems considered to disjunctive programs with infinitely many terms also known as reverse convex programs and give necessary and sufficient conditions for the solution sets of such problems to be sequentially convexifiable we point out important classes of problems in addition to facial disjunctive programs for instance reverse convex programs with equations only for which the conditions are always satisfied finally we give examples of disjunctive programs for which the conditions are violated and so the procedure breaks down

the heat equation shrinking convex plane curves soient m et m des varietes de riemann et f m m une application reguliere si m est une courbe convexe plongee dans le plan r 2 l equation de la chaleur contracte m a un point

generalized intersection cuts and a new cut generating paradigm intersection cuts are generated from a polyhedral cone and a convex set s whose interior contains no feasible integer point we generalize these cuts by replacing the cone with a more general polyhedron c the resulting generalized intersection cuts dominate the original ones this leads to a new cutting plane paradigm under which one generates and stores the intersection points of the extreme rays of c with the boundary of s rather than the cuts themselves these intersection points can then be used to generate in a non recursive fashion cuts that would require several recursive applications of some standard cut generating routine a procedure is also given for strengthening the coefficients of the integer constrained variables of a generalized intersection cut the new cutting plane paradigm yields a new characterization of the closure of intersection cuts and their strengthened variants this characterization is minimal in the sense that every one of the inequalities it uses defines a facet of the closure

an exact approach to the one dimensional facility layout problem the one dimensional facility layout problem is concerned with arranging n departments of given lengths on a line while minimizing the weighted sum of the distances between all pairs of departments the problem is np hard because it is a generalization of the minimum linear arrangement problem in this paper a 0 1 quadratic programming model consisting of only o n2 0 1 variables is proposed for the problem subsequently this model is cast as an equivalent mixed integer program and then reduced by preprocessing next additional redundant constraints are introduced and linearized in a higher space to achieve an equivalent mixed 0 1 linear program whose continuous relaxation provides an approximation of the convex hull of solutions to the quadratic program it is shown that the resulting mixed 0 1 linear program is more efficient than previously published mixed integer formulations in the computational results several problem instances taken from the literature were efficiently solved to optimality moreover it is now possible to efficiently solve problems of a larger size

pauli equation and the method of supersymmetric factorization we consider different variants of factorization of a 2 2 matrix schrodinger pauli operator in two spatial dimensions they allow us to relate its spectrum to the sum of spectra of two scalar schrodinger operators in a manner similar to one dimensional darboux transformations we consider both the case when such factorization is reduced to the ordinary two dimensional supersymmetric quantum mechanics quasifactorization and a more general case which involves covariant derivatives the admissible classes of electromagnetic fields are described and some illustrative examples are given

evolving a convex closed curve to another one via a length preserving linear flow abstract motivated by a recent curvature flow introduced by professor s t yau s t yau private communication on his curvature difference flow 2007 we use a simple curvature flow to evolve a convex closed curve to another one under the assumption that both curves have the same length we show that under the evolution the length is preserved and if the curvature is bounded above during the evolution then an initial convex closed curve can be evolved to another given one

exploiting special structures in constructing a hierarchy of relaxations for 0 1 mixed integer problems a new hierarchy of relaxations is presented that provides a unifying framework for constructing a spectrum of continuous relaxations spanning from the linear programming relaxation to the convex hull representation for linear mixed integer 0 1 problems this hierarchy is an extension of the reformulation linearization technique rlt of sherali and adams 1990 1994a and is particularly designed to exploit special structures specifically inherent special structures are exploited by identifying particular classes of multiplicative factors that are applied to the original problem to reformulate it as an equivalent polynomial programming problem and subsequently this resulting problem is linearized to produce a tighter relaxation in a higher dimensional space this general framework permits us to generate an explicit hierarchical sequence of tighter relaxations leading up to the convex hull representation a similar hierarchy can be constructed for polynomial mixed integer 0 1 problems additional ideas for further strengthening rlt based constraints by using conditional logical implications as well as relationships with sequential lifting are also explored several examples are presented to demonstrate how underlying special structures including generalized and variable upper bounding covering partitioning and packing constraints as well as sparsity can be exploited within this framework for some types of structures low level relaxations are exhibited to recover the convex hull of integer feasible solutions

an additive bounding procedure for the asymmetric travelling salesman problem in this paper new lower bounds for the asymmetric travelling salesman problem are presented based on spanning arborescences the new bounds are combined in an additive procedure whose theoretical performance is compared with that of the balas and christofides procedure 1981 both procedures have been imbedded in a simple branch and bound algorithm and experimentally evaluated on hard test problems

projections of the capacitated network loading problem abstract consider an undirected network and a set of commodities with specified demands between various pairs of nodes of the network given two types of capacitated facilities that can be installed loaded for arc dependent costs we have to determine the integer number of facilities to load on each arc in order to send the required flow of all commodities at minimum total cost we present a natural mixed integer programming formulation of the problem and then consider its single commodity and multicommodity versions we develop equivalent formulations in a lower dimensional space by projecting out the flow variables and study the polyhedral properties of the corresponding projection cones our results strengthen an existing result for multicommodity flow problems we also characterize several classes of facet defining inequalities for this lower dimensional polyhedron and conclude by identifying some open problems and future research directions

polynomial programming lp relaxations also converge we consider the global minimization of a multivariate polynomial on a compact semialgebraic set using a result of krivine j analyse math 12 1964 pp 307 326 c r acad sci paris 258 1964 pp 3417 3418 it is shown that lp relaxations based on products of the original constraints in the spirit of the reformulation linearization technique procedure of sherali and adams converge to the global optimum this extends to compact semialgebraic sets previous results known for polytopes and 0 1 programs the asymptotic behavior of the lp relaxations is also analyzed and it is shown that in important cases finite convergence cannot occur