较多约束多目标规划的最优性条件

本文研究较多约束多目标规划的最优性条件.借助于所给问题的较多约束集结构表示,定义了较多约束规划问题的较多约束Pareto有效解和较多约束Pareto弱有效解,给出较多约束Pareto有效解和较多约束Pareto弱有效解要满足的Fritz John条件和Kuhn-Tucker条件,最后给出在凸性条件下它的一些最优性充分条件.     

关于多目标数学规划的最优性条件

本文讨论定义于Ｂａｎａｃｈ空间的多目标数学规划，得到一些ε－最优解和（弱）有效解的必要条件，充分条件和必要充分条件。     

ε－次可微多目标规划的最优性条件

本文主要从多目标规划相应的加权问题出发，讨论了在ε－次可微的条件下，凸多目标规划问题η－有效解存在的必要条件与充分条件．     

不可微多目标规划的最优性条件

众所周知,Clarke、Ioffe和Aubin对非光滑分析做出了开创性的奠基工作,然而当应用它们解决有关实际问题时,在不少情况下还不很理想,特别是,他们所定义的向量函数广义梯度都比较难计算,这常造成相应不可微多目标规划算法在具体实现时的困难。     

n—集合函数多目标规划的最优性条件

本文在广义ρ－凸的条件下给出了ｎ集合函数多目标规划解的必要和充分条件。     

二层多目标规划的最优性条件

本文在集值优化的框架下提出了一个二层多目标规划模型（BLMOP）.利用集值映射的相依导数和相依上导数,给出了几个有关（BLMOP）的弱有效解的必要或充分最优性条件.     

广义多目标minmax问题的最优性条件和极大熵方法

本文讨论了广义多目标minmax问题的最优性条件。利用极大熵逼近函数，研究了广义多目标minmax；问题的逼近问题，在较弱的条件下，证明了由极大熵逼近函数导出的多目标逼近问题的临界点的任一极限点均为原广义多目标minmax问题的临界点。     

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.     

非光滑多目标优化问题的最优性条件

本文利用极值原理在Fréchet次微分下研究了非光滑多目标优化问题的最优性条件.首先,研究了非光滑半无限多目标优化问题的必要性条件.随后,建立了非光滑多目标优化问题Henig真有效解的必要条件.     

Optimality Conditions for C1,1 Vector Optimization Problems

The main purpose of this paper is to make use of the second-order subdifferential of vector functions to establish necessary and sufficient optimality conditions for vector optimization problems.     

Optimality Conditions for C 1,1 Constrained Multiobjective Problems

The present paper is concerned with the study of the optimality conditions for constrained multiobjective programming problems in which the data have locally Lipschitz Jacobian maps. Second-order necessary and sufficient conditions for efficient solutions are established in terms of second-order subdifferentials of vector functions.     

C1,1半定规划的二阶最优性条件

研究了C1,1函数类的半定规划问题,其中的目标函数是连续可微的,其梯度是拟可微的.利用拟可微分析分别给出了二阶必要条件和二阶充分条件.     

Second-Order Optimality Conditions in Generalized Semi-Infinite Programming

This paper deals with generalized semi-infinite optimization problems where the (infinite) index set of inequality constraints depends on the state variables and all involved functions are twice continuously differentiable. Necessary and sufficient second-order optimality conditions for such problems are derived under assumptions which imply that the corresponding optimal value function is second-order (parabolically) directionally differentiable and second-order epiregular at the considered point. These sufficient conditions are, in particular, equivalent to the second-order growth condition.     

Second-Order Optimality Conditions for Set-Valued Vector Equilibrium Problems

In this article, by using the generalized second-order contingent (adjacent) epiderivatives of set-valued maps, we obtain necessary optimality conditions and sufficient optimality conditions for weakly efficient solutions, Henig efficient solutions to the set-valued vector equilibrium problems with constraints. Some results of this article improve the corresponding results in literatures by lessening the assumption of convexity.     

广义半无限规划新的最优性条件

本文讨论了一类指标集依赖于决策变量的广义半无限规划(GSMMP).首先通过刻画目标函数的Clarke导数和Clarke次微分,建立其一阶最优性条件.其次,通过对下层问题Q(x)进行扰动分析,我们得到Q(x)的一个精确罚表示.由此,利用一组精确罚函数将(GSMMP)转化为经典的半无限极大极小规划,从而可利用已有的经典半无限规划的算法来对(GSMMP)进行求解.     

模糊多目标半定规划

This paper first applies the fuzzy set theory to multi-objective semi-definite program-ming （MSDP）, and proposes the fuzzy multi-objective semi-definite programming （FMSDP） model whose optimal efficient solution is defined for the first time, too. By constructing a membership function, the FMSDP is translated to the MSDP. Then we prove that the optimal efficient solution of FMSDP is consistent with the efficient solution of MSDP and present the optimality condition about these programming. At last, we give an algorithm for FMSDP by introducing a new membership function and a series of transformation.     

Second-Order Optimality Conditions in Multiobjective Optimization Problems

In this paper, we develop second-order necessary and sufficient optimality conditions for multiobjective optimization problems with both equality and inequality constraints. First, we generalize the Lin fundamental theorem (Ref. 1) to second-order tangent sets; then, based on the above generalized theorem, we derive second-order necessary and sufficient conditions for efficiency.     

不可微向量优化问题严有效解的最优性条件

本文研究向量优化问题在严有效解意义下的最优性条件.在局部凸Hausdorff拓扑线性空间中.在近似锥一次类凸假设下,利用凸集分离定理得到了最优性必要条件.借助Gateaux导数引进了几种新的凸性,在新的凸性假设下得到了最优性充分条件.     

一类G-(F,ρ)凸多目标分式规划的最优性条件

本文讨论了一类多目标分式规划问题，其中所包含的函数是局部Lipschitz的和Clarke次可微的．首先，在G-(F，ρ)凸的条件下，证明了择一定理．然后，证明了该多目标分式规划问题在Geoffrion意义下的真有效解的充分条件和必要条件．