OPTIMALITY CONDITIONS IN NONSMOOTH MULTIOBJECTIVE PROGRAMMING

ＯＰＴＩＭＡＬＩＴＹＣＯＮＤＩＴＩＯＮＳＩＮＮＯＮＳＭＯＯＴＨＭＵＬＴＩＯＢＪＥＣＴＩＶＥＰＲＯＧＲＡＭＭＩＮＧ￥ＷＡＮＧＬｉａｎｃｈｅｎｇ；ＤＯＮＧＪｉａｌｉ；ＬＩＵＱｉｎｇｈｕａｉ（ＤｅｐｅｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＪｉｌｉｎＵｎｉ...     

DUALITY FOR A CLASS OF NONSMOOTHMULTIOBJECTIVE PROGRAMMING PROBLEMS

In this paper, two new dual models of nonsmooth multiobjective programmingare constructed and two duality results are derived.     

THE SECOND-ORDER CONDITIONS OF NONDOMINATED SOLUTIONS FOR C~(1,?) GENERALIZED MULTIOBJECTIVE MATHEMATICAL PROGRAMMING

In this paper,the generalized Hessian matrix and the generalized second-order directional(?)erivative for C~(1,1)vector functions are defined.The extension of the vector second-order Taylorexpansion is derived.The second-order necessary and sufficient conditions for the local nondominatedsolutions associated with the given convex cone and polyhedral convex cone of the generalizedmultiobjective mathematical programming problem with C~(1,1)constrained functions are discussed.     

SYMMETRIC DUALITY FOR A CLASS OF MULTIOBJECTIVE FRACTIONAL PROGRAMMING

1.IntroductionSymmetricdualityinnonlinearprogrammingwasintroducedbyDorn,whodefinedaprogramanditsdualtobesymmetricifthedualofthedualistheoriginalproblem;thatis,ifwhenthedualprogramisrecastintheformoftheprimal,itsdualistheprimal.Alinearprogramanditsdualares…     

递阶多目标非光滑优化问题的最优性条件

建立了递阶多目标非光滑优化问题的一个通用性结构化模型,利用参数规划、集值分析及非光滑非线性分析的理论和方法,研究了模型锥有效解存在的最优必要条件和充分条件．     

NECESSARY CONDITIONS FOR MAJOR OPTIMAL SOLUTIONS AND MAJOR EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING

1.IntroductionThestudyofnecessaryconditionforvariousefficielltsolutionsofmultiobjectiveprogrammingisanimportantaridfundamentalsubject.Notonlytheseconditionsleadtokeyeffectivenesswhensomealgorithmsareprovidedwiththem,butalsotheyareimportantandusefultoolsto…     

动态非光滑Nash协商解必要条件的研究

本文利用非光滑分析理论，采用公理化方法研究了非光滑情形下的动态协商对策问题，给出其Ｎａｓｈ协商解的必要条件，并给予了严格的数学证明．     

一类新型的指派问题的多目标模型

针对传统的指派问题在实际应用中的局限性，提出了一类新型的指派问题，基于其特殊性建立了相应的多目标模型，并通过化为单目标问题而获得的有效解，同时，模型学考虑了给被分配者有多次选择机会的情形，最后给出实例分析。     

NONCONICAL NONSMOOTH MULTIOBJECTIVE PROGRAMMING-OPTIMALITY CONDITIONS AND

1.IntroductionLetRpbeapdimellsionalEuclideanspace,KanirreflekivebinaryrelationonRp.ForyEgr,thelowersection0fy(w.r-tK)istheset(`y)={y'ly'Ky}.TheinteriorrelationK'of`isdefinedasy,`"yifandonlyify'EIllt(Ky)(Int,Clmeaninteriorandclosure0faset).Letf:Rn- Rp,g:R"- RmbelocallyLipschitzvector-valuedfunctions(i.e.eachcomponelltofthemislocallyLipschitz),Kaclosedc0nvexpointedconewithnonemptyinieri0rinRm.SetX={xER"lg(x)E-K}.TheMultiobjectiveProgramming,withf,X,Kasobjectivefuncti0n,feasiblesetan…     

OPTIMALITY CONDITIONS AND DUALITY THEOREMS IN NONCONICAL MULTIOBJECTIVE PROGRAMMING

ＯＰＴＩＭＡＬＩＴＹＣＯＮＤＩＴＩＯＮＳＡＮＤＤＵＡＬＩＴＹＴＨＥＯＲＥＭＳＩＮＮＯＮＣＯＮＩＣＡＬＭＵＬＴＩＯＢＪＥＣＴＩＶＥＰＲＯＧＲＡＭＭＩＮＧＬＩＹｕａｎｘｉ（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓａｎｄＯＲ，ＦｕｄａｎＵｎｉｖｅｒｓｉ...     

New results about the relationship between optimally weighted least squares estimate and linear minimum variance estimate

The optimally weighted least squares estimate and the linear minimum variance estimate are two of the most popular estimation methods for a linear model. In this paper, the authors make a comprehensive discussion about the relationship between the two estimates. Firstly, the authors consider the classical linear model in which the coefficient matrix of the linear model is deterministic, and the necessary and sufficient condition for equivalence of the two estimates is derived. Moreover, under certain conditions on variance matrix invertibility, the two estimates can be identical provided that they use the same a priori information of the parameter being estimated. Secondly, the authors consider the linear model with random coefficient matrix which is called the extended linear model; under certain conditions on variance matrix invertibility, it is proved that the former outperforms the latter when using the same a priori information of the parameter. This research is supported in part by the National Natural Science Foundation of China under Grant Nos. 60232010, 60574032, and the Project 863 under Grant No. 2006AA12A104.     

多层线性规划问题可行解的充要条件和单纯形算法

研究多层线性规划问题。先对可行解提出几个必要与充分条件, 然后在这些条件的基础上设计出一种单纯形算法。最后通过求解一个三层规划问题为例来说明这种方法。     

USING DISPLACED CONE REPRESENTATION IN DEA MODELS FOR NONDOMINATED SOLUTIONSIN MULTIOBJECTIVE PROGRAMMING

1.IlltroductionBowlin,etal.[2]extendedtheearlierworkofBowlinetal.11]aspartofaresponsetowhatseemstobeagrowinginterestintheuseofefficiencydominance--asreflected,forexampleintheworkofLoved[7],TulkensandVandenEeckaut[lo]andtheirassociates.ThefocusinBowlinetal.[2]turnedtotheuseofan11metricasabasisfor(1)measuringtheamountofefficiencydominancethatmightbepresentinanyDecisionMakingUnit(DMU)aswellasfor(2)dealingwithproblemsinvolvedinthepossiblepresenceofslackswithnon-zerovalues,--whichareimportantas…     

A NECESSARY AND SUFFICIENT CONDITION FOR A POINT TO BE A GLOBAL MAXIMIZER OF A CONSTRAINED OPTIMIZATION

It is difficult to judge whether a given point is a global maximizer of an unconstrained optimization problem. This paper deals with this problem by considering global information via integral and gives a necessary and sufficient condition judging whether a given point is a global maximizer of an unconstrained optimization problem. An algorithm is offered under such a condition and finally two test problems are verified via the offered algorithm.     

非光滑多目标Stackelberg问题的最优性条件

本文研究非光滑多目标Ｓｔａｃｋｅｌｂｅｒｇ问题，给出其有关性质及最优性必要条件，并对若干特例进行了讨论．     

多目标线性规划的一种矩阵对策方法

提出了一种求解多目标线性规划问题的人机对话方法，其基本原理与ＳＴＥＭ方法大致相同，但采用了两人零和混合对策思想确定Ｔｃｈｅｂｙｃｈｅｖ距离中的相对权重，使权重的确定方法较传统的机械式相对固定权重确定方法更为合理     

A NEW METHOD FOR FINDING MAJOR EFFICIENT SOLUTIONS AND MAJOR OPTIMAL SOLUTIONS OFDISCRETE MULTIOBJECTIVE PROGRAMMING

1.IntroductionThetermefficiencyisalsoknownasadmissibility,ornoninferiority.Itdepictsthemultiobjectiveprogrammingfromtheangleofsatisfaction.Majorefficiencyisbasedonthelawofmajority,whichhasbeenilitensivilyinvestigatedinpapers[1--3].Theprimaryconceptsaremajorefficientsolutionandmajoroptimalsolution.Considerthefollowingmultiobjectiveprogramming:whereXCR"isthefeasibleregion,f:X~ac,f(x)=(fi(x),f200,'',fm(x))",andfi:X~Risareal-valuedfunction,acandacareEuclideanspaces.oIntroducetwoconesetsHandH…     

THE COMPARISON-NUMBER METHOD FOR FINDING MAJOR OPTIMAL SOLUTIONS AND MAJOR EFFICIENT SOLUTIONS OF THE DISCRETE MULTIOBJECTIVE PROGRAMMING

In this paper, we introduce the comparison number for one feasible solutioncompared with another. With the help of it the comparison-number method for find-ing the major optimal solutions aud major efficient solutions to discrete multiobjectiveprogramming is given.     

Sufficiency and duality for nonsmooth multiobjective programming problems involving generalized univex functions

In this paper, nonsmooth univex, nonsmooth quasiunivex, and nonsmooth pseudounivex functions are introduced. By utilizing these new concepts, sufficient optimality conditions for a weakly efficient solution of the nonsmooth multiobjective programming problem are established. Weak and strong duality theorems axe also derived for Mond-Weir type multiobjective dual programs.     

多准则、多目标决策评价系统的设计与实现

以导弹系统设计方案评应用为背景,针对多准则、多目标的决策问题,研究和设计系统化的决策评价体系,完成具有核心功能的,通用性、实用性较好的多准则、多目标决策评价工具,对复杂的决策问题提供决策支持。