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.     

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.     

PROPER EFFICIENT SOLUTIONS AND PROPER SADDLE POINTS

This paper offers a characterization method for the proper efficient solution ofthe multiobjective programming problem in terms of the proper saddle point and proves anecessary and sufficient condition for the equivalence between the proper efficient solutionand the associated proper saddle point by using the duality of a pair of problems.     

OPTIMALITY CONDITIONS AND DUALITY THEOREMS IN NONCONICAL MULTIOBJECTIVE PROGRAMMING

ＯＰＴＩＭＡＬＩＴＹＣＯＮＤＩＴＩＯＮＳＡＮＤＤＵＡＬＩＴＹＴＨＥＯＲＥＭＳＩＮＮＯＮＣＯＮＩＣＡＬＭＵＬＴＩＯＢＪＥＣＴＩＶＥＰＲＯＧＲＡＭＭＩＮＧＬＩＹｕａｎｘｉ（ＤｅｐａｒｔｍｅｎｔｏｆＳｔａｔｉｓｔｉｃｓａｎｄＯＲ，ＦｕｄａｎＵｎｉｖｅｒｓｉ...     

SYMMETRIC DUALITY FOR A CLASS OF MULTIOBJECTIVE FRACTIONAL PROGRAMMING

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

GENERALIZED SUBCONVEXLIKE FUNCTIONS AND MULTIPLE OBJECTIVE OPTIMIZATION

ＧＥＮＥＲＡＬＩＺＥＤＳＵＢＣＯＮＶＥＸＬＩＫＥＦＵＮＣＴＩＯＮＳＡＮＤＭＵＬＴＩＰＬＥＯＢＪＥＣＴＩＶＥＯＰＴＩＭＩＺＡＴＩＯＮ￥ＹＡＮＧＸｉｎｍｉｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＣｈｏｎｇｑｉｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔ...     

The Class of the Generalized αk-Major Efficient Solutions for Multi-objective Programming

1 IntroductionConsider the following multi--objective programming:V -- minf(x) Cl)x e xwhere XcrR" is a constrained set, and f: R"-R"(m22) is the vector objective function.A non--dominated solution for (1 ) is usually called the Pareto efficient solution. HuL1jintroduced the concepts of major efficient solutions and major optimal solutions, thenpresented the concepts of a--major efficient so1utions and a--major optimal solutions. Ma[2Jgave a genera1ization of the major optimal solutions, a…     

SOME RATIONALITY CONDITIONS OF JOINT EFFICIENT MAPPING IN GROUP MULTI-OBJECTIVE PROGRAMMING

The joint efficient ordering method is a fundamental method of ordering alternatives in group multi-objective programming problems. In this paper, the rational properties of the joint efficient mapping corresponding to the joint efficient ordering method are studied, and some necessary conditions of this mapping are proven.     

收益率为模糊数的加权证券组合选择模型

Markowitz基于概率理论建立了有名的均值方差证券组合模型，文章则基于模糊理论建立了一类具有权系数的均值方差证券组合模型，首先对证券市场上的收益与风险特性重新进行度量和刻画，提出了一类新的具有加权的可能性均值、方差及协方差的概念，类似于概率论中均值方差的分析讨论了这些概念的性质．其次基于该文定义的均值方差，建立了以收益率为模糊数的加权可能性证券组合投资模型，并给出了相应的加权可能性有效证券组合及有效前沿概念，通过求解两个相对应的优化模型得到了一个具有带状投资区域的有效前沿．尤其当资产收益率具有线性或分段线性隶属函数的模糊数时，该证券组合选择模型实质上为一个线性规划问题，因此有效前沿可化为一个具有折线段的带状投资区域。     

Connectedness of G—proper Efficient Solution Set for Multiobjective Programming Problem

1　 IntroductionWe know that one of the mostimportant problems of multiobjective programming is to in-vestigate the structure of efficientsolution sets. Among the topological properties of thesesets,connectedness is of interest.In Euclidean space,many results have been obtainedabout the connectedness of efficient solution set in past.The set of efficient solution isconnected when the objective functions are strictly quasiconcave[1 ] .In general,efficientsolution set is so large for multiobjec…     

基于VRS的SE-DEA模型可行性的研究

通过一种改进的DEA模型——SE-DEA模型可以对决策单元进行充分比较和排序，但在可变规模收益(VRS)条件下，这种模型可能不存在可行解，定义了超有效和强超有效决策单元，对基于VRS的SE-DEA模型的可行性进行了研究，证明了评价某决策单元的SE-DEA(VRS)模型是不可行的充分必要条件是该决策单元为超有效，给出了用SE-DEA(VRS)模型对决策单元进行评价与排序的方法步骤，将决策单元按强超有效、超有效、一般有效和非有效进行排序，最后将这些理论与方法应用于评价产业经济相对有效性的实际。     

二层线性规划的有效解

在容许集有界且二层线性规划存在最优解是相应双目标规划有效解的假设下,证明了有效最优解可在容许集的顶点达到。给出了二层线性规划的解的更为合理的有效化方法,并用算例对各种有效化方法所得的有效解进行了比较。     

基于粗集理论的多目标规划问题的约束度分析

给出了有冗余约束条件的多目标规划问题的模型约简方法。对于无冗余约束条件的决策系统 ,决策者可通过对约束条件的重要性分析而按其重要性大小适当删除不重要约束 ,从而得到原问题的核心约束条件组和相应核心有效解。原问题的有效解和核心有效解的关系可以用粗糙近似来刻画。用算例说明了这种方法的应用。     

上海证券市场日期效应检验及其有效性的研究

以随机选取的沪市18支典型股票的收益率为样本，通过对任意两类日收益率及其残差的统计分析及其日期效应的研究，结果表明：上海证券市场存在着较为明显的日期效应。这一结果支持了目前学术界关于上海证券市场弱有效性的观点。     

DEA有效的最速性

对非ＤＥＡ有效的决策单元，本文定义了其ＤＥＡ有效的最速性及相关概念，讨论了它的一些性质，给出了计算方法及实例。     

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…     

基于扩展有效的逆DEA模型

为了克服决策单元在有效性的评价和排序方面占主导地位的缺陷,在扩展DEA模型的基础上,对于输出减少时的逆DEA问题进行了讨论.通过求解相应的多目标规划问题(VP),得到了多目标规划(VP)的Pareto弱有效解与评价减少了输出的决策单元的规划问题的最优值之间的一些相关性质.对于决策单元为弱DEA有效的情形,也进行了类似的讨论.最后用数值实例加以说明.     

Portfolio Selection with Random Liability and Affine Interest Rate in the Mean-Variance Framework

This paper studies a dynamic mean-variance portfolio selection problem with random liability in the affine interest rate environment, where the financial market consists of three assets: one risk-free asset, one risky asset and one zero-coupon bond. Assume that short rate is driven by affine interest rate model and liability process is described by the drifted Brownian motion, in addition, stock price dynamics is affected by interest rate dynamics. The investors expect to look for an optimal strategy to minimize the variance of the terminal surplus for a given expected terminal surplus. The efficient strategy and the efficient frontier are explicitly obtained by applying dynamic programming principle and Lagrange duality theorem. A numerical example is given to illustrate our results and some economic implications are analyzed.     

Several Modulation in Direct-Sequence Spectrum-Spread Systems

1 .ＩＮＴＲＯＤＵＣＴＩＯＮＤｉｒｅｃｔ ｓｅｑｕｅｎｃｅｓｐｒｅａｄ ｓｐｅｃｔｒｕｍ (ＤＳ ＳＳ)ｉｓａｍｏｎｇｔｈｅｍｏｓｔｐｒｏｍｉｓｉｎｇｔｅｃｈｎｉｑｕｅｓｉｎｍｏｂｉｌｅｃｏｍｍｕｎｉｃａｔｉｏｎｓｙｓｔｅｍｓｗｈｅｒｅｅａｃｈｕｓｅｒｕｓｅｓａｄｉｓｔｉｎｃｔｉｖｅｓｐｒｅａｄｉｎｇｓｅｑｕｅｎｃｅａｓｉｔｓａｄｄｒｅｓｓｃｏｄｅ.Ｉｎｔｈｅｔｒａｎｓｍｉｔｔｅｒ,ｂａｓｅｂａｎｄｓｉｇｎａｌｓｓｈｏｕｌｄｂｅｍｏｄｕｌａｔｅｄｆｏｒｔｒａｎｓｍｉｓｓｉｏｎｉｎｗｉｒｅｌｅｓｓｃｈａｎ…     

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.