拓扑向量空间中非光滑向量极值问题的最优性条件与对偶

本文提出了向量值函数的锥D-s凸，锥D-s拟凸，s右导数及锥D-s伪凸等新概念，探讨了锥D-s凸函数的有关性质，建立了带约束非光滑向量极值问题(VP)的最优性必要条件与涉及锥D-s凸(拟凸，伪凸)函数的约束极值问题(VP)的最优性充分条件，给出了原问题(VP)与其Mond-Weir型对偶问题的弱对偶与强对偶结论，揭示了(VP)的局部锥D-(弱)有效解与整体锥D-(弱)有效解，(VP)的锥D-弱有效解与锥D-有效解的关系，所得结果拓广了凸规划及部分广义凸规划的有关结论．     

近似次微分刻画的约束向量均衡问题的最优性条件北大核心CSCD

该文研究一类约束向量均衡问题(CVEP)近似拟弱有效解的最优性条件和对偶定理.首先,建立了问题(CVEP)近似拟弱有效解关于近似次微分形式的最优性必要条件.其次,引入了一种广义凸性的概念,称之为近似伪拟type-I函数,并在其假设下,获得了问题(CVEP)近似拟弱有效解的最优性充分条件.最后,引入了问题(CVEP)的广义近似Mond-Weir对偶模型,并建立其与原问题间关于近似拟弱有效解的对偶定理.     

锥拟凸集值映射多目标优化的解集的连通性

在一般拓扑向量空间中,本文引进了一类锥进凸（锥严格拟凸）集值映射。并在目标映射是锥拟凸（锥严格拟凸）和上半连续的条件下,利用Minkowski泛函,证明了弱有效解（有效解）集是连通的。文[9]中的结论是本文所得结果大目标映射为单值和拓扑空间为格的情况下的特例。     

多目标锥—广义凸规划有效解的充要条件

本文提出了ｎ维欧氏空间上的锥－凸、锥－伪凸、锥－拟凸向量值函数的概念，讨论了它们之间的关系，并在此基础上，对多目标数学规划问题关于凸锥∧有效解，撇开约束品性，讨论了它的充分必要条件。     

D-E-半预不变真拟凸映射与向量优化

提出了一类新的向量值映射-D-E-半预不变真拟凸映射,它是D-半预不变真拟凸映射和D-E-预不变真拟凸映射的真推广.首先,举例验证了D-E半预不变真拟凸映射的存在性;其次,说明了D-E-半预不变真拟凸映射的水平集是E-半不变凸集,讨论了D-E-严格半预不变真拟凸映射和D-E-半严格半预不变真拟凸映射的关系;再次,在D-E-半严格(严格)半预不变真拟凸性下,得出了向量优化问题的E-局部有效解为E-全局有效解,E-局部弱有效解为E-全局弱有效解,并举例验证了所得结果;最后,在D-E-严格半预不变真拟凸性下,建立了向量优化问题的E-全局弱有效解和E-局部弱有效解的唯一性刻画.     

拟凸多目标优化问题近似解的最优性条件

研究了拟凸多目标优化问题近似弱有效解、近似有效解的最优性条件.首先,在已有拟凸函数次微分的基础上引进4种近似次微分的概念,并给出它们之间的关系.然后,将4种近似次微分的概念应用到拟凸多目标优化问题中,给出了拟凸多目标优化问题近似弱有效解和近似有效解的充分条件和必要条件,并给出实例加以说明.     

D-η-半预不变真拟凸多目标优化的最优性刻画

首先,举例验证了三种D-η-半预不变真拟凸映射的存在性;然后,在D-η-半严格(严格)半预不变真拟凸性下,得出了多目标优化问题的局部有效解为全局有效解,局部弱有效解为全局弱有效解,并举例验证了所得结果;最后,在D-η-严格半预不变真拟凸性下,建立了多目标优化问题的全局弱有效解和局部弱有效解的唯一性的刻画。     

D-η-半预不变真拟凸多目标优化的最优性刻画

首先,举例验证了三种D-η-半预不变真拟凸映射的存在性;然后,在D-η-半严格(严格)半预不变真拟凸性下,得出了多目标优化问题的局部有效解为全局有效解,局部弱有效解为全局弱有效解,并举例验证了所得结果;最后,在D-η-严格半预不变真拟凸性下,建立了多目标优化问题的全局弱有效解和局部弱有效解的唯一性的刻画。     

非光滑半无限多目标规划弱非控解的充分性

本文利用锥次微分的概念，在一点处定义了η－（Ａ，Ｎ）凸函数、η－（Ａ，Ｎ）伪凸函数和η－（Ａ，Ｎ）严格伪凸函数，在相当弱的假设下，在η－（Ａ，Ｎ）意义下，给出了非光滑η－（Ａ，Ｎ）凸半无限多目标规划弱非控解的一些充分条件。     

本刊外文版11卷2期文章简介（1995）

本刊外文版１１卷２期文章简介（１９９５）Ｗ￣ｋ，ｐ（Ω，■）（ｋ■１）中的多重积分的半连续性张承钿，李开泰该文证明了Ｗ‘，”拟凸性是Ｃａｒａｔｈｅｏｄｏｒｙ函数多重积分弱下半连续（弱”是下半连续）的充分和必要条件，如有界变分函数０５人ｘ，。Ｊ三ｇ（，...     

Optimality Conditions for Isolated Local Minimum of Nonsmooth Multiobjective Problems

This article is devoted to the study of Fritz John and strong Kuhn-Tucker necessary conditions for properly efficient solutions, efficient solutions and isolated efficient solutions of a nonsmooth multiobjective optimization problem involving inequality and equality constraints and a set constraints in terms of the lower Hadamard directional derivative. Sufficient conditions for the existence of such solutions are also provided where the involved functions have pseudoconvex sublevel sets. Our results are based on the concept of pseudoconvex sublevel sets. The functions with pseudoconvex sublevel sets are a class of generalized convex functions that include quasiconvex functions.     

非光滑多目标广义本性凸规划的最优性条件与对偶

In this paper, we introduce generalized essentially pseudoconvex function and generalized essentially quasiconvex function, and give sufficient optimality conditions of the nonsmooth generalized convex multi-objective programming and its saddle point theorem about cone efficient solution. We set up Mond-Weir type duality and Craven type duality for nonsmooth multiobjective programming with generalized essentially convex functions, and prove them.     

非光滑向量极值问题的真有效解与最优性条件

讨论了赋范线性空间中非光滑向量极值问题的Hatley,Borwein,Benson真有效解之间的关系,指出了它们共同的标量极值问题的等价刻画,建立了问题（VMP）的广义KT-真有效解的充分条件,并给出了向量极小值问题在锥局部凸、拟凸、伪凸等条件下的最优性条件。     

Optimality via generalized approximate convexity and quasiefficiency

In this article, we look beyond convexity and introduce the four new classes of functions, namely, approximate pseudoconvex functions of type I and type II and approximate quasiconvex functions of type I and type II. Suitable examples illustrating the non emptiness of the newly defined classes and distinguishing them from the existing classical notions of pseudoconvexity and quasiconvexity are provided. These newly defined concepts are then employed to establish sufficient optimality conditions for the quasi efficient solutions of a vector optimization problem.     

拟凸函数的近似次微分及其在多目标优化问题中的应用

针对拟凸函数提出一类新的近似次微分,研究其性质,并将近似次微分应用到拟凸多目标优化问题近似解的刻画中.首先,对已有的近似次微分进行改进,得到拟凸函数新的近似次微分,并给出其与已有次微分之间的关系及一系列性质.随后,利用新的近似次微分给出拟凸多目标优化问题近似有效解、近似真有效解的最优性条件.     

On the functions with pseudoconvex sublevel sets and optimality conditions

A new class of generalized convex functions, called the functions with pseudoconvex sublevel sets, is defined. They include quasiconvex ones. A complete characterization of these functions is derived. Further, it is shown that a continuous function admits pseudoconvex sublevel sets if and only if it is quasiconvex. Optimality conditions for a minimum of the nonsmooth nonlinear programming problem with inequality, equality and a set constraints are obtained in terms of the lower Hadamard directional derivative. In particular sufficient conditions for a strict global minimum are given where the functions have pseudoconvex sublevel sets.     

Convexifactors, Generalized Convexity, and Optimality Conditions

The recently introduced notion of a convexifactor is further studied, and quasiconvex and pseudoconvex functions are characterized in terms of convexifactors. As an application to a chain rule, a necessary optimality condition is deduced for an inequality constrained mathematical programming problem.     

Sufficient optimality criteria in nonlinear programming for generalized equality-inequality constraints

Sufficient optimality criteria of the Kuhn-Tucker and Fritz John type in nonlinear programming are established in the presence of equality-inequality constraints. The constraint functions are assumed to be quasiconvex, and the objective function is taken to be pseudoconvex (or convex).     

Second-order Kuhn-Tucker invex constrained problems

A new notion of a second-order KT invex problem (P) with inequality constraints is introduced in this paper. This class of problems strictly includes the KT invex ones. Some properties of the second-order KT invex problems are presented. For example, (P) is second-order KT invex if and only if each point, which satisfies the second-order Kuhn-Tucker necessary optimality conditions, is a global minimizer. A problem with quasiconvex data is (second-order) KT invex if and only if it is (second-order) KT pseudoconvex.