The Alternative Property and Vector Optimization Problem in Ordered Locally Convex Topological Vector Spaces

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Optimality and Duality for Nondifferentiable Multiple-Objective Optimization with Generalized Univexity

1　 IntroductionFor the following nonlinear programming problem( P) min f( x)subjectto　　 g( x) 0　　If there exists a vector functionη( x,x0 ) such thatf( x) -f( x0 ) [ f( x0 ) ] Tη( x,x0 )-g( x0 ) [ g( x0 ) ] Tη( x,x0 )for all x,x0 ∈ S={x|g( x) 0 },then,f( x) and g( x) are said to type objective and type constraint functions[1 ] .Hanson and Mond[1 ] obtained sufficient and necessary optimality conditions andduality results.Reuda,Hanson[2 ] further extended type functions to pseu…     

线性分式—二次双层规划的对偶定理

先给出线性分式规划的一个对偶定理,然后利用这个结果建立和证明线性分式—二次双层规划的对偶定理。     

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.     

SYMMETRIC DUALITY FOR A CLASS OF MULTIOBJECTIVE FRACTIONAL PROGRAMMING

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

A MODIFIED HOMOGENEOUS AND SELF-DUAL LINEAR PROGRAMMING ALGORITHM

ＡＭＯＤＩＦＩＥＤＨＯＭＯＧＥＮＥＯＵＳＡＮＤＳＥＬＦ－ＤＵＡＬＬＩＮＥＡＲＰＲＯＧＲＡＭＭＩＮＧＡＬＧＯＲＩＴＨＭ￥ＧＵＯＴｉａｎｄｅ（ＭａｔｈｅｍａｔｉｃｓＤｅｐａｒｔｍｅｎｔ，ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｑｕｆｕ２７３１６５，Ｃｈ...     

不确定退出时间和随机市场环境下风险资产的动态投资组合选择

本文在不确定退出时间和随机市场环境下利用拉格朗日对偶方法研究了多阶段均值-方差投资组合选择问题.我们假定市场上的资产全是风险资产,且随机市场环境只有有限个自然状态,自然状态的转移过程为时变马尔可夫链,各阶段资产的随机收益率不仅与时间有关而且与市场所处的状态有关.首先利用动态规划技术和拉格朗日对偶方法得到了模型的有效投资策略及有效边界的显式表达式.然后,还给出并证明了一个多阶段版本的两基金分离定理,最后,为说明本文的结论及应用,给出了一个数值算例.     

OPTIMALITY CONDITIONS AND DUALITY THEOREMS IN NONCONICAL MULTIOBJECTIVE PROGRAMMING

ＯＰＴＩＭＡＬＩＴＹＣＯＮＤＩＴＩＯＮＳＡＮＤＤＵＡＬＩＴＹＴＨＥＯＲＥＭＳＩＮＮＯＮＣＯＮＩＣＡＬＭＵＬＴＩＯＢＪＥＣＴＩＶＥＰＲＯＧＲＡＭＭＩＮＧＬＩＹｕａｎｘｉ（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓａｎｄＯＲ，ＦｕｄａｎＵｎｉｖｅｒｓｉ...     

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.     

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…     

MATHEMATICAL PROGRAMMING WITH A CLASS OF NON-SMOOTH FUNCTIONS

1 IntroductionIn 1981, H..,.,,[1] introduced the notion of invexity aJnd showed that for inequality con-strained programs, Karush~Kuhn-Tucker(KKT) conditions are sufficient fOr optimality if thefunctions involved are invex(differentiable) functiolis. Sinc…     

MINIMAX PROGRAMMING UNDER GENERALIZED （p, r）-INVEXITY

Minimax programming problems involving generalized （p, r）-invex functions are consid- ered. Parametric sufficient optimality conditions and duality results are established under the aforesaid assumptions on the objective and constraint functions.     

我国上市公司董事会结构对R&D投入的影响

以2004～2007年披露R&D投入的790个上市公司为样本观察值,构建了多元线性回归模型,研究上市公司的董事会结构与R&D投入的关系.结果表明:研发投入与董事会素质正相关,董事会素质越高,R&D投入越大;当执行董事的比例在1/10～1/3时,或当董事长与总经理两职分任时,独立董事比例越高,越会弱化执行董事之间在R&D战略决策及监督管理层执行R&D活动的知识协同效应,导致R&D投入越小;具有研发、设计和营销等职业背景的董事长和第2影响力董事,往往从企业长远利益出发,其越年轻越倾向于增加R&D投入;董事长与总经理两职分任,会降低R&D投入.     

ANALYSIS OF INCOMPLETE STOCK MARKET WITH JUMP-DIFFUSION UNCERTAINTY

This paper studies incomplete stock market that includes discontinuous price processes. The discontinuity is modeled by very general point processes admitting only stochastic intensities. Prices are driven by jump-diffusion uncertainty and have random but predictable jumps. The space of risk-neutral measures that are associated with the market is identified and related to fictitious completions. The construction of replicating portfolios is discussed, and convex duality methods are used to prove existence of optimal consumption and investment policies for a problem of utility maximization.     

新的Lagrangian松弛法求解CLSP问题

ＣＬＳＰ是在受能力约束限制下，确定Ｎ种不同的项目在给定的计划范围Ｔ内的第一时间段批量，使得在整个计划范围内项目总的调整费用和库存保管费用以及生产费用之和最小。     

大规模含整变量多目标决策基于目标期望水平的交互式分解协调方法

针对具有块角结构的大规模含整变量多目标决策问题提出了一种基于目标期望水平的交互多分解协调方法。该方法利用目标期望水平实现交互决策过程。利用拉格朗日分解对偶方法进行分解协协调。文中定义了若干概念，证明了若干定理，给出了交互决策的具体步骤，并对软件实现作了说明.     

EQUIVALENT CONDITIONS FOR THE UNIFORM CONTINUITY OF DUALITY MAPPING

InII],T.Katogaveasufficientconditionfortheuniformcontinuityofdualitymapping,in[2],MaShaoqinpointedoutthattheconversepropositionofthisresultholdstoo.[3]gotthattheuniformcontinuityofdualitymappingF(x)isequivalenttothat(F(x ty),y),(F(x),y),(t~0)uniformlyforx…     

关于整数线性规划代理对偶间隙的注记

将有效不等式的概念应用于整数线性规划的代理对偶问题 ,给出弥合整数线性规划的代理对偶间隙的方法 .数值例子表明所给出的方法在改进定界结果方面是有效的 .     

或有要求权的定价方法及无套利价格区间

在多时间段的框架下，采用完全套期保值原理、线性规划对偶原理和鞋理论给出了或有要求权的卖方套利价格和买方套利价格的计算方法，分别对允许证券卖空、现金借贷和不允许征券卖空、只允许现金借贷的情况进行了研究。相应的套利价格和无套利价格区间可以通过递推求解有限个线性规划问题得到。     

Generalized invexity-type conditions in constrained optimization

This paper defines a new class of generalized type I functions, and obtains Kuhn-Tucker necessary and sufficient conditions and duality results for constrained optimization problems in the presence of the aforesaid weaker assumptions on the objective and constraint functions involved in the problem.