inference based sensitivity analysis for mixed integer linear programming a new method of sensitivity analysis for mixed integer linear programming milp is derived from the idea of inference duality the inference dual of an optimization problem asks how the optimal value can be deduced from the constraints in milp a deduction based on the resolution method oftheorem proving can be obtained from the branch and cut tree that solves the primal problem one can then investigate which perturbations ofthe problem leave this proof intact on this basis it is shown that in a minimization problem any perturbation that satisfies a certain system of linear inequalities will reduce the optimal value no more than a prespecified amount one can also give an upper bound on the increase in the optimal value that results from a given perturbation the method is illustrated on two realistic problems

constructing solutions for the prescribed scalar curvature problem via local pohozaev identities abstract this paper deals with the following prescribed scalar curvature problem u q y y u n 2 n 2 u 0 y y y r 2 r n 2 where q y is nonnegative and bounded by combining a finite reduction argument and local pohozaev type of identities we prove that if n 5 and q r y has a stable critical point r 0 y 0 with r 0 0 and q r 0 y 0 0 then the above problem has infinitely many solutions whose energy can be made arbitrarily large here instead of estimating directly the derivatives of the reduced functional we apply some local pohozaev identities to locate the concentration points of the bump solutions moreover the concentration points of the bump solutions include a saddle point of q y

the c 3 theorem and a d 2 algorithm for large scale stochastic mixed integer programming set convexification this paper considers the two stage stochastic integer programming problem with an emphasis on instances in which integer variables appear in the second stage drawing heavily on the theory of disjunctive programming we characterize convexifications of the second stage problem and develop a decomposition based algorithm for the solution of such problems in particular we verify that problems with fixed recourse are characterized by scenario dependent second stage convexifications that have a great deal in common we refer to this characterization as the c3 common cut coefficients theorem based on the c3 theorem we develop a decomposition algorithm which we refer to as disjunctive decomposition d2 in this new class of algorithms we work with master and subproblems that result from convexifications of two coupled disjunctive programs we show that when the second stage consists of 0 1 milp problems we can obtain accurate second stage objective function estimates after finitely many steps this result implies the convergence of the d2 algorithm

a finite branch and bound algorithm for two stage stochastic integer programs this paper addresses a general class of two stage stochastic programs with integer recourse and discrete distributions we exploit the structure of the value function of the second stage integer problem to develop a novel global optimization algorithm the proposed scheme departs from those in the current literature in that it avoids explicit enumeration of the search space while guaranteeing finite termination computational experiments on standard test problems indicate superior performance of the proposed algorithm in comparison to those in the existing literature

probabilistic analysis of a generalized bin packing problem and applications we give a unified probabilistic analysis for a general class of bin packing problems by directly analyzing corresponding mathematical programs in this general class of packing problems objects are described by a given number of attribute values some attributes may be discrete others may be continuous bins are sets of objects and the collection of feasible bins is merely required to satisfy some general consistency properties we characterize the asymptotic optimal value as the value of an easily specified linear program whose size is independent of the number of objects to be packed or as the limit of a sequence of such linear program values we also provide bounds for the rate of convergence of the average cost to its asymptotic value the analysis suggests an a s asymptotically optimal heuristic that runs in linear time the heuristics can be designed to be asymptotically optimal while still running in polynomial time we also show that in several important cases the algorithm has both po

disjunctive decomposition for two stage stochastic mixed binary programs with random recourse this paper introduces disjunctive decomposition for two stage mixed 0 1 stochastic integer programs sips with random recourse disjunctive decomposition allows for cutting planes based on disjunctive programming to be generated for each scenario subproblem under a temporal decomposition setting of the sip problem a new class of valid inequalities for mixed 0 1 sip with random recourse is presented in particular we derive valid inequalities that allow for scenario subproblems for sip with random recourse but deterministic technology matrix and right hand side vector to share cut coefficients the valid inequalities are used to derive a disjunctive decomposition method whose derivation has been motivated by real life stochastic server location problems with random recourse which find many applications in operations research computational results with large scale instances to demonstrate the potential of the method are reported

convex analysis in groups and semigroups a sampler we define convexity canonically in the setting of monoids we show that many classical results from convex analysis hold for functions defined on such groups and semigroups rather than only vector spaces some examples and counter examples are also discussed

integer programming duality price functions and sensitivity analysis recently a duality theory for integer programming has been developed here we examine some of the economic implications of this theory in particular the necessity of using price functions in place of prices and the possibility of carrying out sensitivity analysis of optimal solutions in addition we consider the form of price functions that are generated by known algorithms for integer programming

an updated table of minimum distance bounds for binary linear codes in 1973 helgert and sfinaff published a table of upper and lower bounds on the maximum minimum distance for binary linear error correcting codes up to length 127 this article presents an updated table incorporating numerous improvements that have appeared since then to simplify the updating task the author has developed a computer program that systematically investigates the consequences of each improvement by applying several well known general code construction techniques this program also made it possible to check the original table furthermore it offers a quick and reliable update service for future improvements

finitely convergent decomposition algorithms for two stage stochastic pure integer programs we study a class of two stage stochastic integer programs with general integer variables in both stages and finitely many realizations of the uncertain parameters based on benders method we propose a decomposition algorithm that utilizes gomory cuts in both stages the gomory cuts for the second stage scenario subproblems are parameterized by the first stage decision variables i e they are valid for any feasible first stage solutions in addition we propose an alternative implementation that incorporates benders decomposition into a branch and cut process in the first stage we prove the finite convergence of the proposed algorithms we also report our preliminary computations with a rudimentary implementation of our algorithms to illustrate their effectiveness

on the 162 8 80 codes constructions of 162 8 80 and 159 8 78 codes are given this solves the open problems of finding the minimum length of binary codes of dimension s and minimum distances 78 and 80 respectively

asymptotic strong duality for bounded integer programming a logarithmic exponential dual formulation a logarithmic exponential dual formulation is proposed in this paper for bounded integer programming problems this new dual formulation possesses an asymptotic strong duality property and guarantees the identification of an optimal solution of the primal problem these prominent features are achieved by exploring a novel nonlinear lagrangian function deriving an asymptotic zero duality gap investigating the unimodality of the associated dual function and ensuring the primal feasibility of optimal solutions in the dual formulation one other feature of the logarithmicexponential dual formulation is that no actual dual search is needed when parameters are set above certain threshold values

computing discrete logarithms in high genus hyperelliptic jacobians in provably subexponential time we provide a subexponential algorithm for solving the discrete logarithm problem in jacobians of high genus hyperelliptic curves over finite fields its expected running time for instances with genus g and underlying finite field fq satisfying g log q for a positive constant is given by o e f 1 3 2 3 2 o 1 g log q log g log q the algorithm works over any finite field and its running time does not rely on any unproven assumptions

sensitivity theorems in integer linear programming we consider integer linear programming problems with a fixed coefficient matrix and varying objective function and right hand side vector among our results we show that for any optimal solution to a linear program max wx ax b the distance to the nearest optimal solution to the corresponding integer program is at most the dimension of the problem multiplied by the largest subdeterminant of the integral matrixa using this we strengthen several integer programming proximity results of blair and jeroslow graver and wolsey we also show that the chvatal rank of a polyhedron x ax b can be bounded above by a function of the matrixa independent of the vectorb a result which as blair observed is equivalent to blair and jeroslow s theorem that each integer programming value function is a gomory function

variation of cost functions in integer programming we study the problem of minimizingc x subject toa x b x 0 andx integral for a fixed matrixa two cost functionsc andc are considered equivalent if they give the same optimal solutions for eachb we construct a polytopest a whose normal cones are the equivalence classes explicit inequality presentations of these cones are given by the reduced grobner bases associated witha the union of the reduced grobner bases asc varies called the universal grobner basis consists precisely of the edge directions ofst a we present geometric algorithms for computingst a the graver basis and the universal grobner basis

concentration compactness phenomena in the higher order liouville s equation we investigate different concentration compactness and blow up phenomena related to the q curvature in arbitrary even dimension we first treat the case of an open domain in r 2 then that of a closed manifold and finally the particular case of the sphere s 2m in all cases we allow the sign of the q curvature to vary and show that in the case of a closed manifold contrary to the case of open domains in r 2m blow up phenomena can occur only at points of positive q curvature as a consequence on a locally conformally flat manifold of non positive euler characteristic we always have compactness

the role of the green s function in a non linear elliptic equation involving the critical sobolev exponent this paper is concerned with non linear elliptic problems of the type pe u u n 2 n 2 eu u 0 on u 0 on where is a smooth and bounded domain in rn n 4 and e 0 we show that if the ue are solutions of pe which concentrate around a point as e 0 then this point cannot be on the boundary of and is a critical point of the regular part of the green s function conversely we show that for n 5 and any non degenerate critical point x0 of the regular part of the green s function there exist solutions of pe concentrating around x0 as e 0

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

decomposition algorithms with parametric gomory cuts for two stage stochastic integer programs we consider a class of two stage stochastic integer programs with binary variables in the rst stage and general integer variables in the second stage we develop decomposition algorithms akin to the l shaped or benders methods by utilizing gomory cuts to obtain iteratively tighter approximations of the second stage integer programs we show that the proposed methodology is exible in that it allows several modes of implementation all of which lead to nitely convergent algorithms we illustrate our algorithms using examples from the literature we report computational results using the stochastic server location problem instances which suggest that our decomposition based approach scales better with increases in the number of scenarios than a state of the art solver which was used to solve the deterministic equivalent formulation

computing discrete logarithms in real quadratic congruence function fields of large genus the discrete logarithm problem in various finite abelian groups is the basis for some well known public key cryptosystems recently real quadratic congruence function fields were used to construct a public key distribution system the security of this public key system is based on the difficulty of a discrete logarithm problem in these fields in this paper we present a probabilistic algorithm with subexponential running time that computes such discrete logarithms in real quadratic congruence function fields of sufficiently large genus this algorithm is a generalization of similar algorithms for real quadratic number fields

blow up phenomena for scalar flat metrics on manifolds with boundary abstract let m n g be a compact riemannian manifold with boundary m this article is concerned with the set of scalar flat metrics on m which are in the conformal class of g and have m as a constant mean curvature hypersurface we construct examples of metrics on the unit ball b n in dimensions n 25 for which this set is non compact these manifolds have umbilic boundary but they are not conformally equivalent to b n

computing the sign or the value of the determinant of an integer matrix a complexity survey computation of the sign of the determinant of a matrix and the determinant itself is a challenge for both numerical and exact methods we survey the complexity of existing methods to solve these problems when the input is an n n matrix a with integer entries we study the bit complexities of the algorithms asymptotically in n and the norm of a existing approaches rely on numerical approximate computations on exact computations or on both types of arithmetic in combination

feasibility of integer knapsacks given a matrix a in mathbb z m times n satisfying certain regularity assumptions we consider the set mathcal f a of all vectors boldsymbol b in mathbb z m such that the associated knapsack polytope p a boldsymbol b boldsymbol x in mathbb r n geq0 a boldsymbol x boldsymbol b contains an integer point when m 1 the set mathcal f a is known to contain all consecutive integers greater than the frobenius number associated with a in this paper we introduce the diagonal frobenius number mathrm g a which reflects in an analogous way feasibility properties of the problem and the structure of mathcal f a in the general case we give an optimal upper bound for mathrm g a and also estimate the asymptotic growth of the diagonal frobenius number on average

a shadow price in integer programming for management decision abstract the main purpose of this paper is to propose a new concept of shadow prices in integer programming with rich economic interpretation which is useful in management decision and to examine closely some related properties as well as computational methods this shadow price is based not on marginal analysis but on average analysis the existence and the uniqueness that have not been achieved until now from other studies on dual prices of integer programming are guaranteed for this shadow price a version of complementary slackness theorem in integer programming has been achieved for this shadow price an easy method of finding upper and lower bounds of the shadow price as well as a rigorous algorithm of obtaining its exact value is presented

hermite and smith normal form algorithms over dedekind domains we show how the usual algorithms valid over euclidean domains such as the hermite normal form the modular hermite normal form and the smith normal form can be extended to dedekind rings in a sequel to this paper we will explain the use of these algorithms for computing in relative extensions of number fields

decomposition with branch and cut approaches for two stage stochastic mixed integer programming decomposition has proved to be one of the more effective tools for the solution of large scale problems especially those arising in stochastic programming a decomposition method with wide applicability is benders decomposition which has been applied to both stochastic programming as well as integer programming problems however this method of decomposition relies on convexity of the value function of linear programming subproblems this paper is devoted to a class of problems in which the second stage subproblem s may impose integer restrictions on some variables the value function of such integer subproblem s is not convex and new approaches must be designed in this paper we discuss alternative decomposition methods in which the second stage integer subproblems are solved using branch and cut methods one of the main advantages of our decomposition scheme is that stochastic mixed integer programming smip problems can be solved by dividing a large problem into smaller mip subproblems that can be solved in parallel this paper lays the foundation for such decomposition methods for two stage stochastic mixed integer programs

the constraints of the group of an integral monoid abstract a z module group of integral vectors can be constrained by subspace and integrality constraints we show how to extract these constraints from the chvatal constraints of an integral monoid

l shaped decomposition of two stage stochastic programs with integer recourse we consider two stage stochastic programming problems with integer recourse the l shaped method of stochastic linear programming is generalized to these problems by using generalized benders decomposition nonlinear feasibility and optimality cuts are determined via general duality theory and can be generated when the second stage problem is solved by standard techniques finite convergence of the method is established when gomory s fractional cutting plane algorithm or a branch and bound algorithm is applied

logic based benders decomposition benders decomposition uses a strategy of learning from one s mistakes the aim of this paper is to extend this strategy to a much larger class of problems the key is to generalize the linear programming dual used in the classical method to an inference dual solution of the inference dual takes the form of a logical deduction that yields benders cuts the dual is therefore very different from other generalized duals that have been proposed the approach is illustrated by working out the details for propositional satisfiability and 0 1 programming problems computational tests are carried out for the latter but the most promising contribution of logic based benders may be to provide a framework for combining optimization and constraint programming methods

on the computation of unit groups and class groups of totally complex quartic fields in this paper we describe the computation of a system of fundamental units and of the class group for each totally real quartic field y of discriminant less than 106 generating equations integral bases and the galois groups for all those fields were recently given by buchmann and ford

marginal values in mixed integer linear programming for a given optimization problem p considered as a function of the data its marginal values are defined as the directional partial derivatives of the value of p with respect to perturbations in that data for linear programs formulas for the marginal values were given by mills 10 and further developed by the current author 16 in this paper the marginal value formulas are extended to the case of mixed integer linear programming mip as in ordinary linear programming discontinuities in the value can occur and the analysis here identifies them this latter aspect extends previous work on continuity by the current author 18 geoffrion and nauss 5 nauss 11 and radke 12 and work on the value function of blair and jeroslow 2 application is made to model formulation and to post optimal analysis

a geometric buchberger algorithm for integer programming let ip a c denote the family of integer programs of the form min cx ax b x nn obtained by varying the right hand side vector b but keeping a and c fixed a test set for ipa c is a set of vectors in zn such that for each nonoptimal solution to a program in this family there is at least one element g in this set such that g has an improved cost value as compared to we describe a unique minimal test set for this family called the reduced grobner basis of ip a c an algorithm for its construction is presented which we call a geometric buchberger algorithm for integer programming and we show how an integer program may be solved using this test set the reduced grobner basis is then compared with some other known test sets from the literature we also indicate an easy procedure to construct test sets with respect to all cost functions for a matrix a zn 2 n of full row rank

recognizing badly presented z modules finitely generated z modules have canonical decompositions when such modules are given in a finitely presented form there is a classical algorithm for computing a canonical decomposition this is the algorithm for computing the smith normal form of an integer matrix we discuss algorithms for smith normal form computation and present practical algorithms which give excellent performance for modules arising from badly presented abelian groups we investigate such issues as congruential techniques sparsity considerations pivoting strategies for gauss jordan elimination lattice basis reduction and computational complexity our results which are primarily empirical show dramatically improved performance on previous methods

hermite normal form computation using modulo determinant arithmetic this paper describes a new class of hermite normal form solution procedures which perform modulo determinant arithmetic throughout the computation this class of procedures is shown to possess a polynomial time complexity bound which is a function of the length of the input string computational results are also given

prescribing scalar curvature on s3 s4 and related problems abstract we show that for the prescribing scalar curvature problem on sn n 3 4 we can perturb in an explicit way any given positive continuous function in any neighborhood of any given point on sn such that for the perturbed function there exist many solutions the related critical exponent equations u k x u n 2 n 2 in rn n 3 4 with k x being asymptotically periodic in one of the variables are also studied and infinitely many positive solutions modulo translations by its periods are obtained under some additional mild hypotheses on k x some a priori estimates to solutions of the prescribing scalar curvature problem on s3 are as given

algorithms for computing a hermite reduction of a matrix with polynomial coefficients resume nous etudions dans cet article des algorithmes de calcul de la reduction de hermite d une matrice a coefficients polynomiaux qui evitent l explosion de la taille des objets intermediaires et ont une bonne complexite sequentielle le deuxieme et le troisieme algorithmes generalisent la methode des sous resultants pour le calcul du pgcd de deux polynomes le dernier de ces algorithmes semble optimal en ce sens qu il calcule une reduction de hermite avec une matrice de passage de degre minimal en utilisant une methode progressive et economique nous ramenons le calcul de la reduite de hermite a un probleme de triangulation progressive des matrices dont les tailles sont bien controlees et dont les entrees sont des coefficients de polynomes donnes en entree l algorithme est donc faisable des qu on dispose d une methode de triangulation en temps polynomial pour les matrices dans le corps des coefficients il revient au meme de dire que le calcul des determinants est en temps polynomial dans le corps en question pour le codage choisi les resultats theorqiues sont meilleurs que pour les algorithmes connus precedemment et les resultats partiques sont encourageants

a compactness theorem for scalar flat metrics on 3 manifolds with boundary abstract let m g be a compact riemannian three dimensional manifold with boundary we prove the compactness of the set of scalar flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface this involves a blow up analysis of a yamabe type equation with critical sobolev exponent on the boundary

a polynomial time algorithm to compute generalized hermite normal forms of matrices over z x abstract in this paper we give the first polynomial time algorithm to compute the generalized hermite normal form for a matrix f over z x or equivalently the reduced grobner basis of the z x module generated by the column vectors of f the algorithm has polynomial bit size computational complexities and is also shown to be practically more efficient than existing algorithms the algorithm is based on three key ingredients first an f4 style algorithm to compute the grobner basis is adopted where a novel prolongation is designed such that the sizes of coefficient matrices under consideration are nicely controlled second the complexity bound of the algorithm is achieved by a nice estimation for the degree and height bounds of the polynomials in the generalized hermite normal form third fast algorithms to compute hermite normal forms of matrices over z are used as the computational tool

new bounds on binary linear codes of dimension eight corresp let n k d be the smallest integer n such that a binary linear code of length n dimension k and minimum distance at least d exists new results are given that improve the best previously known bounds on n 8 d

exact augmented lagrangian duality for mixed integer linear programming we investigate the augmented lagrangian dual ald for mixed integer linear programming mip problems ald modifies the classical lagrangian dual by appending a nonlinear penalty function on the violation of the dualized constraints in order to reduce the duality gap we first provide a primal characterization for ald for mips and prove that ald is able to asymptotically achieve zero duality gap when the weight on the penalty function is allowed to go to infinity this provides an alternative characterization and proof of a recent result in boland and eberhard math program 150 2 491 509 2015 proposition 3 we further show that under some mild conditions ald using any norm as the augmenting function is able to close the duality gap of an mip with a finite penalty coefficient this generalizes the result in boland and eberhard 2015 corollary 1 from pure integer programming problems with bounded feasible region to general mips we also present an example where ald with a quadratic augmenting function is not able to close the duality gap for any finite penalty coefficient

a closed form representation of mixed integer program value functions we identify a class of formulas computable in polynomial time such that the functions defined by these formulas are precisely the value functions of mixed integer programs with rational constraint coefficients

there is no binary 35 10 13 code it is shown that the generator matrix of a putative linear binary code 36 10 14 contains the generator matrix of a 32 7 14 or a 33 8 14 binary linear code in a first step all nonisomorphic 32 7 14 and 33 8 14 binary codes are enumerated then it is shown that none of these codes yields a 35 10 13 linear binary code

two stage integer programs with stochastic right hand sides a superadditive dual approach we consider two stage pure integer programs with discretely distributed stochastic right hand sides we present an equivalent superadditive dual formulation that uses the value functions in both stages we give two algorithms for finding the value functions to solve the reformulation after obtaining the value functions we develop a global branch and bound approach and a level set approach to find an optimal tender we show that our method can solve randomly generated instances whose extensive forms are several orders of magnitude larger than the extensive forms of those instances found in the literature

ground states for a system of schrodinger equations with critical exponent abstract we study the following system of nonlinear schrodinger equations u u u p 1 u v x r n v v v 2 2 v u x r n where n 3 2 2 n n 2 1 p 2 1 and are positive parameters satisfying 0 we show that there is some critical value 0 0 1 such that this system has a positive ground state solution if 0 0 in the case 0 there exists 0 such that this system has no ground state solutions if while this system has a positive ground state solution if in particular if p 2 1 the system has no nontrivial solutions some further properties of the ground state solutions are also studied this seems to be the first result for such a critical schrodinger system

there is no binary 25 8 10 code the existence of a binary 25 8 10 code is considered it is shown that such a code must have a generator matrix of a specific form however all generator matrices of this form were tested and none generated a 25 8 10 code thus such a code does not exist

the value function of an integer program we consider integer programs in which the objective function and constraint matrix are fixed while the right hand side varies the value function gives for each feasible right hand side the criterion value of the optimal solution we provide a precise characterization of the closed form expression for any value function

a fast las vegas algorithm for computing the smith normal form of a polynomial matrix abstract a las vegas probabilistic algorithm is presented that finds the smith normal form s q x n n of a nonsingular input matrix a z x n n the algorithm requires an expected number of o n 3 d d n 2 log a bit operations where a bounds the magnitude of all integer coefficients appearing in a and d bounds the degrees of entries of a in practice the main cost of the computation is obtaining a nonunimodular triangularization of a polynomial matrix of the same dimension and with similar size entries to those of the input matrix we show how to accomplish this in o n 5 d d log a log a bit operations using standard integer polynomial and matrix arithmetic these complexity results improve significantly on previous algorithms in both a theoretical and a practical sense

a rigorous subexponential algorithm for computation of class groups let c d denote the gauss class group of quadratic forms of a negative discriminant d or equivalently the class group of the imaginary quadratic field q a we give a rigorous proof that there exists a las ve gas algorithm that will compute the structure of c d with an expected running time of l d vf2 1 bit operations where l d exp vlog d log log d thus of course also includes the computation of the class number h d the cardinality of c d ibm research division almaden research center k53 802 650 harry road san jose california 95 120 6099 current address k mccurley organization 1423 sandia national laboratories albuquerque new mexico 87185 this content downloaded from 207 46 13 180 on thu 08 sep 2016 05 47 29 utc all use subject to http about jstor org terms

reachability and steering of rolling polyhedra a case study in discrete nonholonomy rolling a ball on a plane is a standard example of nonholonomy reported in many textbooks and the problem is also well understood for any smooth deformation of the surfaces for nonsmoothly deformed surfaces however much less is known although it may seem intuitive that nonholonomy is conserved think e g to polyhedral approximations of smooth surfaces current definitions of nonholonomy are inherently referred to systems described by ordinary differential equations and are thus inapplicable to such systems in this paper we study the set of positions and orientations that a polyhedral part can reach by rolling on a plane through sequences of adjacent faces we provide a description of such reachable set discuss conditions under which the set is dense or discrete or has a compound structure and provide a method for steering the system to a desired reachable configuration robustly with respect to model uncertainties based on ideas and concepts encountered in this case study and in some other examples we provide we turn back to the most general aspects of the problem and investigate the possible generalization of the notion of kinematic nonholonomy to nonsmooth discrete and hybrid dynamical systems to capture the essence of phenomena commonly regarded as nonholonomic at least two irreducible concepts are to be defined of internal and external nonholonomy which may coexist in the same system these definitions are instantiated by examples

two stage quadratic integer programs with stochastic right hand sides we consider two stage quadratic integer programs with stochastic right hand sides and present an equivalent reformulation using value functions we propose a two phase solution approach the first phase constructs value functions of quadratic integer programs in both stages the second phase solves the reformulation using a global branch and bound algorithm or a level set approach we derive some basic properties of value functions of quadratic integer programs and utilize them in our algorithms we show that our approach can solve instances whose extensive forms are hundreds of orders of magnitude larger than the largest quadratic integer programming instances solved in the literature

from periodic ode s to supercritical pde s abstract let m g be an m dimensional compact riemannian manifold without boundary assume c 2 m is such that g is coercive we prove the existence of solutions to the supercritical problems g u u u p u 0 in m g and g u u e u in m g which concentrate along an m 1 dimensional submanifold of m as p and 0 respectively under suitable symmetry assumptions on the manifold m a connection with the solutions of a class of periodic ode s is established

decomposing finitely generated integral monoids by elimination abstract a finitely generated integral monoid can always be decomposed into a finite although generally exponential number of integral monoids having special structure in that their related integer programming feasibility problems can be solved in polynomial time the decomposition can be constructed using an elimination scheme due to presburger and williams that generalizes fourier motzkin elimination

on a level set characterization of the value function of an integer program and its application to stochastic programming we propose a level set approach to characterize the value function of a pure linear integer program with inequality constraints we study theoretical properties of our characterization and show how they can be exploited to optimize a class of stochastic integer programs through a value function reformulation specifically we develop algorithmic approaches that solve two stage multidimensional knapsack problems with random budgets yielding encouraging computational results

an application of the hermite normal form in integer programming abstract a new algorithm for solving integer programming problems is developed it is based on cuts which are generated from the hermite normal form of the basis matrix at a continuous extreme point

parameterisation algorithms for the integer linear programs in binary variables abstract in this paper we consider the integer programmiing problem minimize z x c x subject to ax b x binary roodman appended the objective function z x to the body of the constraints and presented a modified version of the balas additive algorithm by which each fathomed partial solution is attributed to the constraint which caused the fathoming exploiting this information he conducted a ranging analysis i e calculating bounds on the values of the parameters which leave the original optimal solution unchanged and b parameter change analysis i e determining new optimal solutions if any for revised values of the parameters outside the ranging bounds we extend roodman s results and construct parametric functions of the following form let be any parameter of c or b or a and replace by then holding every other parameter of the program fixed and varying in the set of real numbers we construct the parametric function z which matches non overlapping intervals of with optimal solutions this replaces by exact bounds in the linear programming sense the bounds underestimated by roodman s ranging analysis it also determines optimal solutions for any values of rather than for a revised set of values finally some results of computational experience are presented

the smallest length of eight dimensional binary linear codes with prescribed minimum distance let n 8 d be the smallest integer n for which a binary linear code of length n dimension 8 and minimum distance d exists we prove that n 8 18 42 n 8 26 58 n 8 28 61 n 8 30 65 n 8 34 74 n 8 36 77 n 8 38 81 n 8 42 89 and n 8 60 124 after these results all values of n 8 d are known

computing hermite and smith normal forms of triangular integer matrices abstract this paper considers the problem of transforming a triangular integer input matrix to canonical hermite and smith normal form we provide algorithms and prove deterministic running times for both transformation problems that are optimal in the matrix dimension the algorithms are easily implemented assume standard integer arithmetic and admit excellent performance in practice the results presented here lead to a faster algorithm for computing the smith normal form of an arbitrary i e non triangular input matrix

compactness for a class of yamabe type problems on manifolds with boundary abstract in this paper we are interested in studying the set of positive solutions to the following yamabe type problem g u a x u 0 in m u g b x u n 2 u n n 2 on m where m n g is a compact riemannian n manifold n 3 with boundary g is the laplace beltrami operator for g g is the pointing unit outward normal to m a c m and b c m assuming suitable hypotheses on the functions a n 2 4 n 1 r g and b n 2 2 h g where r g denotes the scalar curvature of the metric g and h g is the mean curvature of m we prove some results of compactness for the set of positive solutions to the problem