on partial shadowing of complete pseudo orbits abstract in recent years many new definitions of shadowing using a notion of ergodic or average pseudo orbit were introduced while under the assumption of chain mixing average pseudo orbit usually can be equivalently replaced by pseudo orbit in these definitions of shadowing it is not completely clear when these shadowing properties i e approximation of a pseudo orbit by a real orbit on a sufficiently large set of indices can or cannot occur in this paper we analyze necessary and sufficient conditions for shadowing over a set with positive density or syndetic while we do not provide full characterization a few relations to standard notions from topological dynamics are obtained

lagrangian relaxation guided problem space search heuristics for generalized assignment problems we develop and test a heuristic based on lagrangian relaxation and problem space search to solve the generalized assignment problem gap the heuristic combines the iterative search capability of subgradient optimization used to solve the lagrangian relaxation of the gap formulation and the perturbation scheme of problem space search to obtain high quality solutions to the gap we test the heuristic using different upper bound generation routines developed within the overall mechanism using the existing problem data sets of various levels of difficulty and sizes including the challenging largest instances we observe that the heuristic with a specific version of the upper bound routine works well on most of the benchmark instances known and provides high quality solutions quickly an advantage of the approach is its generic nature simplicity and implementation flexibility

an iterative method for solving a free boundary problem for an infinite journal bearing the hydrodynamic lubrication is concerned with a particular form of creeping flow between surfaces in relative motion where cavitation takes place the determination of the cavitation area is then of a fundamental importance in order to compute the caracteristics of the mechanisms a one dimensional nonlinear elliptic problem is considered the approximate solution is obtained through a process of successive approximations where at each step the non homogenous term of the approximated problem search the cavitation region

the average shadowing property and strong ergodicity abstract let x be a compact metric space and f x x be a continuous map in this paper we prove that if f has the average shadowing property and the minimal points of f are dense in x then f is weakly mixing and totally strongly ergodic as applications we obtain that if f is a distal or lyapunov stable map having the average shadowing property then x is consisting of one point moreover we illustrate that the full shift has the average shadowing property

the generalized assignment problem valid inequalities and facets three classes of valid inequalities based upon multiple knapsack constraints are derived for the generalized assignment problem general properties of the facet defining inequalities are discussed and for a special case the convex hull is completely characterized in addition we prove that a basic fractional solution to the linear programming relaxation can be eliminated by a facet defining inequality associated with an individual knapsack constraint

a lagrangian dual based branch and bound algorithm for the generalized multi assignment problem this paper develops a lagrangian dual based branch and bound algorithm for the generalized multi assignment problem gmap which includes the well known generalized assignment problem gap as a special case in gmap an object may be required to be duplicated in multiple locations we develop a lagrangian dual ascent algorithm for gmap this dual ascent and the subgradient search each possess advantages that can be combined to develop a new lagrangian dual search algorithm the latter algorithm when incorporated into a branch and bound algorithm as the lower bounding scheme can accelerate the search process computational results demonstrate the efficiency and robustness of this branch and bound algorithm not only for gmaps but for gaps that are more difficult than could be solved by previous algorithms

a new method for cavitations approximation in some general lubrication devices we apply in this paper a new numerical method to approximate cavitation phenomenons in some general devices in lubrication theory the proposed method is based on some conservation laws satisfied by lubricants contained in the devices and it combines a method of lines with an iterative algorithm solving at each step a linear problems with regular solutions some l estimations providing convergence results are given and numerical applications to an elastic journal bearing are presented to show the good performance of the method

the average shadowing property and topological ergodicity in this note we prove that a lyapunov stable map having the average shadowing property from a compact metric space onto itself is topologically ergodic but it is not topologically weakly mixing

the surplus inventory matching problem in the process industry we introduce a new problem that arises from operations planning in the process industry this problem involves matching an order book against surplus inventory before production planning it can be formulated by generalizing the multiple knapsack problem along three dimensions i adding assignment restrictions on items that can be assigned to a knapsack ii adding a new attribute called color in this paper to an item and then adding the associated color constraints that restrict the number of distinct colors that can be assigned to a knapsack and iii considering multiple objectives for optimization we formulate the problem provide a result regarding its complexity and report on our computational experience with solving a set of real instances based on data from the operations of a large steel plant we then propose a network flow based heuristic that yields solutions within 3 of optimal or the best known feasible solution this system has been successfully deployed and is now used daily in the mill operations

preservation of shadowing in discrete dynamical systems abstract we look at the preservation of various notions of shadowing in discrete dynamical systems under inverse limits products factor maps and the induced maps for symmetric products and hyperspaces the shadowing properties we consider are the following shadowing h shadowing eventual shadowing orbital shadowing strong orbital shadowing the first and second weak shadowing properties limit shadowing s limit shadowing orbital limit shadowing and inverse shadowing

on the uncapacitated plant location problem i valid inequalities and facets the uncapacitated plant location problem is considered as a node packing problem for this problem several valid inequalities and facets are discussed necessary and sufficient conditions for trivial facets along with necessary conditions for nontrivial facets are derived in addition all of the facets for the case of three plants and three or more destinations are identified

a survey of algorithms for the generalized assignment problem abstract this paper surveys algorithms for the well known problem of finding the minimum cost assignment of jobs to agents so that each job is assigned exactly once and agents are not overloaded all approaches seem to be based on branch and bound with bound supplied through heuristics and through relaxations of the primal problem formulation from the survey one can select building blocks for the design of one s own tailor made algorithm the survey also reveals that although just about every mathematical programming technique was tried on this problem there is still a lack of a representative set of test problems on which competing enumeration algorithms can be compared as well as a shortage of effective heuristics

a new numerical approach of a lubrication free boundary problem a combination of a semidiscretized scheme and an iterative method is applied to a free boundary problem the considered problem is issued from a cavitation model in lubrication theory and treats on the determination of the cavitation area estimates l w which provide the convergence of the approximated solution is obtained finally some numerical test examples are presented to illustrate the good performance of the method

solving 0 1 integer programming problems arising from large scale planning models we present methods that are useful in solving some large scale hierarchical planning models involving 0 1 variables these 0 1 programming problems initially could not be solved with any standard techniques we employed several approaches to take advantage of the hierarchical structure of variables ordered by importance and other structures present in the models critical but not sufficient for success was a strong linear programming formulation we describe methods for strengthening the linear programs as well as other techniques necessary for a commercial branch and bound code to be successful in solving these problems

an approach to the asymmetric multi depot capacitated arc routing problem despite the fact that the capacitated arc routing problems carps received substantial attention in the literature most of the research concentrates on the symmetric and single depot version of the problem in this paper we fill this gap by proposing an approach to solving a more general version of the problem and analysing its properties we present an milp formulation that accommodates asymmetric multi depot case and consider valid inequalities that may be used to tighten its lp relaxation a symmetry breaking scheme for a single depot case is also proposed an extensive numerical study is carried to investigate the properties of the problem and the proposed solution approach

on shadowing ordinary and ergodic the aim of this paper is to introduce the notion of ergodic shadowing for a continuous onto map which is equivalent to the map being topologically mixing and has the ordinary shadowing property in particular we deduce the chaotic behavior of a map with ergodic shadowing property moreover we define some kind of specification property and investigate its relation to the ergodic shadowing property

f sensitivity and multi sensitivity of hyperspatial dynamical systems abstract let f be a continuous self map defined on a compact metric space x and f be a continuous self map naturally induced by f on the hyperspace k x of all nonempty compact subsets of x endowed with a hausdorff metric firstly a few sufficient and necessary conditions to ensure a dynamical system be f sensitive or multi sensitive are obtained then the following results are proved 1 if x f is a non minimal m system then k x f has f s sensitive pairs almost everywhere 2 if k x f or k y g is f sensitive then k x y f g is f sensitive 3 k x y f g is multi sensitive if and only if k x f or k y g is multi sensitive if and only if x f or y g is multi sensitive moreover it is proved that f g is multi sensitive if and only if f or g is multi sensitive this is a positive answer to a question posed in r li and x zhou 2013 18

shadowing internal chain transitivity and α limit sets abstract let f x x be a continuous map on a compact metric space x and let f f and i c t f denote the set of limit sets limit sets and nonempty closed internally chain transitive sets respectively we show that if the map f has shadowing then every element of i c t f can be approximated to any prescribed accuracy by both the limit set and the limit set of a full trajectory furthermore if f is additionally expansive then every element of i c t f is equal to both the limit set and the limit set of a full trajectory in particular this means that shadowing guarantees that f f i c t f where the closures are taken with respect to the hausdorff topology on the space of compact sets whilst the addition of expansivity entails f f i c t f we progress by introducing novel variants of shadowing which we use to characterise both maps for which f i c t f and maps for which f i c t f

on the uncapacitated plant location problem ii facets and lifting theorems several lifting procedures for facets of the uncapacitated plant location problem are discussed also necessary and sufficient conditions for nontrivial facets with 0 1 integer coefficients are derived in addition all of the facets for the case of three or more plants and three destinations are identified

1 k configuration facets for the generalized assignment problem class of facet defining inequalities for the generalized assignment problem is derived these inequalities are based upon multiple knapsack constraints and are derived from 1 k configuration inequalities

a cutting plane algorithm for the linear ordering problem the linear ordering problem is an np hard combinatorial optimization problem with a large number of applications including triangulation of input output matrices archaeological senation minimizing total weighted completion time in one machine scheduling and aggregation of individual preferences in a former paper we have investigated the facet structure of the 0 1 polytope associated with the linear ordering problem here we report on a new algorithm that is based on these theoretical results the main part of the algorithm is a cutting plane procedure using facet defining inequalities this procedure is combined with various heuristics and branch and bound techniques our computational results compare favorably with the results of existing codes in particular we could triangulate all input output matrices of size up to 60 60 available to us within acceptable time bounds

decomposing matrices into blocks in this paper we investigate whether matrices arising from linear or integer programming problems can be decomposed into so called bordered block diagonal form more precisely given some matrix a we try to assign as many rows as possible to some number beta of blocks of size kappa such that no two rows assigned to different blocks intersect in a common column bordered block diagonal form is desirable because it can guide and speed up the solution process for linear and integer programming problems we show that various matrices from the linear programming and mixed integer programming libraries netlib and miplib can indeed be decomposed into this form by computing optimal decompositions or decompositions with proven quality these computations are done with a branch and cut algorithm based on polyhedral investigations of the matrix decomposition problem in practice however one would use heuristics to find a good decomposition we present several heuristic ideas and test their performance finally we investigate the usefulness of optimal matrix decompositions into bordered block diagonal form for integer programming by using such decompositions to guide the branching process in a branch and cut code for general mixed integer programs