on gap functions and duality of variational inequality problems abstract we extend the definition of the gap function defined by auslender for a more general class of variational inequality problems involving some convex function a study of the duality of the extended variational inequality problem and its dual sheds new light on the meaning of gap functions convexity and differentiability of the gap function are also studied and sufficient conditions are derived we also show how the gap functions for the primal and the dual are related by dual fenchel optimization problems

duality for e variational inequalities via the subdifferential calculus abstract based on the properties of the convex e subdifferential calculus we introduce to a general e variational inequality formulated with the help of a set valued operator and a perturbation function a dual one expressed by making use of the fenchel conjugate of the perturbation function under convexity hypotheses we show that the fulfillment of a regularity condition guarantees that the primal e variational inequality is solvable if and only if its dual one is solvable by particularizing the perturbation function we obtain several dual statements and we succeed to generalize and improve a duality scheme recently given by kum kim and lee an example justifying this generalization is also provided among the special instances of the general result we rediscover also the duality scheme concerning variational inequalities due to mosco

lagrangean relaxation based heuristics for lot sizing with setup times we consider a lot sizing problem with setup times where the objective is to minimize the total inventory carrying cost only the demand is dynamic over time and there is a single resource of limited capacity we show that the approaches implemented in the literature for more general versions of the problem do not perform well in this case we examine the lagrangean relaxation lr of demand constraints in a strong reformulation of the problem we then design a primal heuristic to generate upper bounds and combine it with the lr problem within a subgradient optimization procedure we also develop a simple branch and bound heuristic to solve the problem computational results on test problems taken from the literature show that our relaxation procedure produces consistently better solutions than the previously developed heuristics in the literature

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

some deterministic and random vector equilibrium problems in this paper some generalized concepts about semicontinuity and convexity for vector valued bifunctions are introduced a new existence theorem for vector equilibrium problems is proved further a random version of this result is considered applications to cone saddle points random vector optimization random vector variational inequalities and random vector best approximation problems are finally given

a lagrangian based heuristic for the capacitated lot sizing problem in parallel machines this paper addresses the capacitated lot sizing problem involving the production of multiple items on unrelated parallel machines a production plan should be determined in order to meet the forecast demand for the items without exceeding the capacity of the machines and minimize the sum of production setup and inventory costs a heuristic based on the lagrangian relaxation of the capacity constraints and subgradient optimization is proposed initially the heuristic is tested on instances of the single machine problem and results are compared with heuristics from the literature for parallel machines and small problems the heuristic performance is tested against optimal solutions and for larger problems it is compared with the lower bound provided by the lagrangian relaxation

feasibility and solvability of vector variational inequalities with moving cones in banach spaces abstract in this paper we study the feasibility and solvability of vector variational inequalities with moving cones in banach spaces we show that the strict feasibility implies solvability of vector variational inequalities with moving cones under suitable conditions further we show that under suitable conditions the homogeneous vector variational inequality with a moving cone is solvable whenever it is feasible as consequences we obtain the solvability of vector variational inequalities with feasibility assumptions in banach spaces

quasi orthogonal space frequency coding in non coherent cooperative broadband networks so far complex valued orthogonal codes have been used differentially in cooperative broadband networks these codes however achieve less than unitary code rate when utilized in cooperative networks with more than two relays therefore the main challenge is how to construct unitary rate codes for non coherent cooperative broadband networks with more than two relays while exploiting the achievable spatial and frequency diversity in this paper we extend full rate quasi orthogonal codes to differential cooperative broadband networks where channel information is unavailable from this we propose a generalized differential distributed quasi orthogonal space frequency coding dqsfc protocol for cooperative broadband networks our proposed scheme is able to achieve full rate and full spatial and frequency diversity in cooperative networks with any number of relays through pairwise error probability analysis we show that the diversity gain of our scheme can be improved by appropriate code construction and sub carrier allocation based on this we derive sufficient conditions for the proposed code structure at the source node and relay nodes to achieve full spatial and frequency diversity

on generalized vector pre variational and pre quasivariational inequalities in this paper we consider generalized vector pre variational inequality problems as well as vector pre quasivariational inequality problems in abstract space setting we establish several existence results for these two classes of problems by employing the ky fan lemma and a scalarization technique respectively

vector equilibrium problem and vector optimization this paper examines the vector equilibrium model based on a vector cost consideration this is a generalization of the well known wardrop traffic equilibrium principle where road users choose paths based on just a single cost the concept of parametric equilibria is introduced and used to establish relations with parametric complementarity and variational inequality problems relations with some vector optimization problems via scalarization techniques are given under appropriate conditions some solution methods for solving vector equilibrium problems are also discussed

vector variational inequality as a tool for studying vector optimization problems the paper aims to show that a vector variational inequality can be an useful tool for studying a vector optimization problem

grasp heuristic with path relinking for the multi plant capacitated lot sizing problem this paper addresses the independent multi plant multi period and multi item capacitated lot sizing problem where transfers between the plants are allowed this is an np hard combinatorial optimization problem and few solution methods have been proposed to solve it we develop a grasp greedy randomized adaptive search procedure heuristic as well as a path relinking intensification procedure to find cost effective solutions for this problem in addition the proposed heuristics is used to solve some instances of the capacitated lot sizing problem with parallel machines the results of the computational tests show that the proposed heuristics outperform other heuristics previously described in the literature the results are confirmed by statistical tests

the generalized vector quasi variational like inequalities abstract in this paper we introduce and study a class of generalized vector quasi variational like inequality problem gvqvlip involving set valued mappings with certain monotonicity by employing the scalarization technique several existence results for solutions of the gvqvlip are established under noncompact setting in topological vector spaces these new existence results improve unify and generalize many known results for scalar and vector variational inequalities in recent literature

optimality conditions for vector equilibrium problems in this paper we present the necessary and sufficient conditions for weakly efficient solution henig efficient solution globally efficient solution and superefficient solution to the vector equilibrium problems with constraints as applications we give the necessary and sufficient conditions for corresponding solution to the vector variational inequalities and vector optimization problems

second order global optimality conditions for convex composite optimization in recent years second order sufficient conditions of an isolated local minimizer for convex composite optimization problems have been established in this paper second order optimality conditions are obtained of aglobal minimizer for convex composite problems with a non finite valued convex function and a twice strictly differentiable function by introducing a generalized representation condition this result is applied to a minimization problem with a closed convex set constraint which is shown to satisfy the basic constraint qualification in particular second order necessary and sufficient conditions of a solution for a variational inequality problem with convex composite inequality constraints are obtained 1998 the mathematical programming society inc published by elsevier science b v

a generalized vector variational inequality problem with a set valued semi monotone mapping abstract in this paper we first generalize the concept of semi monotonicity for a scalar single valued mapping to the case of a vector set valued mapping then we consider a generalized vector variational inequality problem concerning the vector set valued semi monotone mapping several existence results are obtained by using the kakutani fan glicksberg fixed point theorem which generalize some results for vector variational inequality problems studied in recent years

the existence theorems of solutions for generalized vector valued variational like inequalities the purpose of this paper is to introduce a new kind of variational inequality a generalized vector variational like inequality which includes several classical and well known variational inequalities as special cases as an application of the knaster kuratowski mazurkiewicz principle as extended by fan in 1961 1 we prove that there exist solutions for our generalized vector variational like inequality under reasonable hypotheses these results generalize corresponding results given by chen et al in 2 giannessi 3 harker and pang 4 hartman and stampacchia 5 isac 6 lee et al 7 noor 8 saigal 9 siddiqi et al 10 and yang 11

vector quasivariational inequalities for fuzzy mappings ii abstract this paper is devoted to study the vector variational inequalities for fuzzy mappings by using the fan browder fixed point theorem the selection theorem of yannelis prabhakar 13 and the scalarization method of luc 9 10 some existence theorems for our inequalities are proved

on the generalized vector variational inequality problem abstract in this paper we study vector variational inequalities with set valued mappings the concept of c x pseudomonotone mapping is introduced by employing the fan lemma we establish several existence results the new results extend and unify existence results of vector variational inequalities for single valued operators under the banach space setting

a tabu search heuristic for the capacitated lot sizing problem with set up carryover this paper presents a tabu search heuristic for the capacitated lot sizing problem clsp with set up carryover this production planning problems allows multiple items to be produced within a time period and setups for items to be carried over from one period to the next two interrelated decisions sequencing and lot sizing are present in this problem our tabu search heuristic consists of five basic move types three for the sequencing decisions and two for the lot sizing decisions we allow infeasible solutions to be generated at a penalty during the course of the search we use several search strategies such as dynamic tabu list adaptive memory and self adjusting penalties to strengthen our heuristic we also propose a lower bounding procedure to estimate the quality of our heuristic solution we have also modified our heuristic to produce good solutions for the clsp without set up carryover the computational study conducted on a set of 540 test problems indicates that on average our heuristic solutions are within 12 of a bound on optimality in addition for the set of test problems our results indicate an 8 reduction in total cost through set up carryover

signal constellations for quasi orthogonal space time block codes with full diversity space time block codes stbcs from orthogonal designs proposed by alamouti and tarokh jafarkhani calderbank have attracted considerable attention lately due to their fast maximum likelihood ml decoding and full diversity however the maximum symbol transmission rate of an stbc from complex orthogonal designs for complex signals is only 3 4 for three and four transmit antennas and it is difficult to construct complex orthogonal designs with rate higher than 1 2 for more than four transmit antennas recently jafarkhani tirkkonen boariu hottinen and papadias foschini proposed stbcs from quasi orthogonal designs where the orthogonality is relaxed to provide higher symbol transmission rates with the quasi orthogonal structure the quasi orthogonal stbcs still have a fast ml decoding but do not have the full diversity the performance of these codes is better than that of the codes from orthogonal designs at low signal to noise ratio snr but worse at high snr this is due to the fact that the slope of the performance curve depends on the diversity it is desired to have the quasi orthogonal stbcs with full diversity to ensure good performance at high snr in this paper we achieve this goal by properly choosing the signal constellations specifically we propose that half of the symbols in a quasi orthogonal design are chosen from a signal constellation set a and the other half of them are chosen from a rotated constellation e sup j spl phi a the resulting stbcs can guarantee both full diversity and fast ml decoding moreover we obtain the optimum selections of the rotation angles spl phi for some commonly used signal constellations simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high snrs

approximate duality for vector quasi equilibrium problems and applications abstract in this paper we introduce new versions of dual problems of a vector quasi equilibrium problem with set valued maps and we give an duality result between approximate solutions of the primal and dual problems as the first application of the main result we obtain an duality for a vector quasi equilibrium problem whose solutions are understood in the sense of proper efficiency the second application is devoted to an duality for a vector optimization problem with set valued maps

existence of solutions of generalized vector variational type inequalities with set valued mappings in this paper we introduce a new class of generalized vector variational type inequalities with set valued mappings gvvti first the solvability of generalized vector variational type inequalities without monotone assumption is considered in banach spaces by using brouwer s fixed point theorem second by the introduction of the concepts of pseudomonotone v coercive and h hemicontinuous the solvability of gvvti is obtained with the assumption of h hemicontinuous and pseudomonotone

a lagrangean based heuristic for dynamic multilevel multiitem constrained lotsizing with setup times in this paper a heuristic approach for the dynamic multilevel multiitem lotsizing problem in general product structures with multiple constrained resources and setup times is proposed with the help of lagrangean relaxation the capacitated multilevel multiitem lotsizing problem is decomposed into several uncapacitated single item lotsizing problems from the solutions of these single item problems lower bounds on the minimum objective function value are derived upper bounds are generated by means of a heuristic finite scheduling procedure the quality of the approach is tested with reference to various problem groups of differing sizes

strong vector f complementary problem and least element problem of feasible set abstract in this paper we introduce several classes of strong vector f complementary problems and give some existence results for these problems in banach spaces we also discuss the least element problems of feasible sets and present their relations with the strong vector f complementary problems

solving multi item capacitated lot sizing problems using variable redefinition mixed integer programming models are typically not used to solve realistic sized production scheduling problems because they require exorbitant solution times we impose a useful taxonomy on production scheduling problems and develop alternative formulations for a wide variety of problems within the taxonomy the linear programming relaxation of the new models is very effective in generating bounds we show that these bounds are equal to those that could be generated using lagrangian relaxation or column generation the linear programming bounds increase in effectiveness as the problems become larger perhaps of greatest significance is that practitioners can obtain our results using only standard off the shelf codes such as lindo or mpsx 370 we report computational experience in several computing environments hardware and software on problems with up to 200 products and 10 time periods 2000 0 1 variables

generalized vector variational type inequalities solvabilities of generalized vector variational type inequalities gvvti are discussed in this work first the solvability of gvvti without monotone assumption for mappings is considered in reflexive banach spaces by using brouwer fixed point theorem browder fixed point theorem second the solvability of gvvti with monotone assumption for mappings is considered in reflexive banach spaces by using ky fan lemma

primal dual approach to the single level capacitated lot sizing problem abstract the lagrangean relaxation of the single level capacitated dynamic lot sizing problem can be solved using the primal dual method the algorithm has monotone and finite convergence properties it works as a steepest ascent method a variant of this approach is also studied a heuristic routine used to obtain a feasible solution in each iteration is presented computational experiences show that this method usually yields better solutions than the subgradient method although it requires greater cpu times