多目标规划的Fritz John充分条件

本文首先对广义凸单目标规划的最优解提出一个 Fritz John充分条件 ,然后对广义凸多目标规划的有效解提出一个 Fritz John充分条件     

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.     

集值优化问题ε-严有效解的广义高阶Fritz John型最优性条件

在实赋范线性空间中研究集值优化问题ε-严有效解的广义高阶Fritz John型最优性条件.利用Wang等引入的广义高阶锥方向邻接导数,在内部锥类凸假设下,借助凸集分离定理,获得了带广义不等式约束的集值优化问题ε-严有效解的广义高阶Fritz John型必要和充分条件.     

超有效元意义下集值优化的最优性条件

该文在Hausdorff局部凸拓扑向量空间考虑约束集值优化问题(SOP)在超有效意义下的Fritz John条件和Kuhn-Tucker条件.首先借助集值映射的下半可微的概念给出这种空间中集值映射导数的定义, 据此讨论了超有效元的Fritz John最优性条件.最后, 给出约束集值优化问题(SOP)取得超有效元的充分条件.     

集值优化问题Benson真有效解的高阶Fritz John型最优性条件

本文讨论的是集值优化问题Benson真有效解的高阶Fritz John型最优性条件,利用Aubin和Fraukowska引入的高阶切集和凸集分离定理,在锥-似凸映射的假设条件下,获得了带广义不等式约束的集值优化问题Benson真有效解的高阶Fritz John型必要和充分性条件.     

有效解的刻划

对于多目标问题有效解的刻划,已有许多工作,在[3]中推广了[5]中单目标凸规划的极优解的 Fritz John 型必要条件,在 Slater 型条件假定下,进一步给出了多目标非可微凸规划有效解的必要条件(本文(7),(8)).[2]在假定 Slater 型条件成立时,证明类似于[3]的条件(本文(9),(10))可成为有效解的充要条件.考虑问题     

非光滑非凸多目标规划解的充分条件

Kuhn-Tucker型条件的充分性一直是最优化理论中引人注意的一个问题.本文对非光滑函数提出了几个非凸概念,然后,讨论了非光滑非凸多目标规划中Kuhn-Tucker型条件和Fritz John型条件的充分性,在很弱的条件下,建立了一系列充分条件.     

拟可微函数优化的Lagrange乘子与一阶最优性条件

本文给出了拟可微优化的Fritz John必须条件与Shapiro最优性必要条件的等价性质以及两个最优性充分条件.     

向量映射的鞍点和Lagrange对偶问题

本文研究拓扑向量空间广义锥-次类凸映射向量优化问题的鞍点最优性条件和Lagrange对偶问题,建立向量优化问题的Fritz John鞍点和Kuhn-Tucker鞍点的最优性条件及其与向量优化问题的有效解和弱有效解之间的联系。通过对偶问题和向量优化问题的标量化刻画各解之间的关系,给出目标映射是广义锥-次类凸的向量优化问题在其约束映射满足广义Slater约束规格的条件下的对偶定理。     

非凸多目标规划有效解的充分条件

本文对于含有η－凸性函数的多目标规划问题的有效解，提出若干充分条件，它们是单目标问题最优解相应充分条件的推广．     

Separations and Optimality of Constrained Multiobjective Optimization via Improvement Sets

In this paper, we investigate the separations and optimality conditions for the optimal solution defined by the improvement set of a constrained multiobjective optimization problem. We introduce a vector-valued regular weak separation function and a scalar weak separation function via a nonlinear scalarization function defined in terms of an improvement set. The nonlinear separation between the image of the multiobjective optimization problem and an improvement set in the image space is established by the scalar weak separation function. Saddle point type optimality conditions for the optimal solution of the multiobjective optimization problem are established, respectively, by the nonlinear and linear separation methods. We also obtain the relationships between the optimal solution and approximate efficient solution of the multiobjective optimization problem. Finally, sufficient and necessary conditions for the (regular) linear separation between the approximate image of the multiobjective optimization problem and a convex cone are also presented.     

群体多目标决策联合有效解类的不变凸充分条件

对于群体多目标决策问题，文[1]引进它的联合有效解类的概念，并给出这类解的最优性必要条件，在对于问题的目标函数和约束函数附加凸性的条件下，文[2]又给出了联合有效解类的最优性充分条件，本文进一步在目标函数和约束函数具不变凸和不变广义 凸的情况下，分别给出了联合有效解类的若干最优性充分条件。     

UNIFORM APPROXIMATION OF A MULTIOBJECTIVE OPTIMIZATION SEQUENCE

In this paper the Pareto efficiency of a uniformly convergent multiobjective optimization sequence is studied. We obtain some relation between the Pareto efficient solutions of a given multiobjective optimization problem and those of its uniformly convergent optimization sequence and also some relation between the weak Pareto efficient solutions of the same optimization problem and those of its uniformly convergent optimization sequence. Besides, under a compact convex assumption for constraints set and a certain convex assumption for both objective and constraint functions, we also get some sufficient and necessary conditions that the limit of solutions of a uniformly convergent multiobjective optimization sequence is the solution of a given multiobjective optimization problem.     

Weak sharp efficiency in multiobjective optimization

By using the generalized Fermat rule, the Mordukhovich subdifferential for maximum functions, the fuzzy sum rule for Fréchet subdifferentials and the sum rule for Mordukhovich subdifferentials, we establish a necessary optimality condition for the local weak sharp efficient solution of a constrained multiobjective optimization problem. Moreover, by employing the approximate projection theorem, and some appropriate convexity and affineness conditions, we also obtain some sufficient optimality conditions respectively for the local and global weak sharp efficient solutions of such a multiobjective optimization problem.     

Generalized asymptotic functions in nonconvex multiobjective optimization problems

In this paper, we use generalized asymptotic functions and second-order asymptotic cones to develop a general existence result for the nonemptiness of the proper efficient solution set and a sufficient condition for the domination property in nonconvex multiobjective optimization problems. A new necessary condition for a point to be efficient or weakly efficient solution is given without any convexity assumption. We also provide a finer outer estimate for the asymptotic cone of the weakly efficient solution set in the quasiconvex case. Finally, we apply our results to the linear fractional multiobjective optimization problem.     

多目标规划的整体解

本文在较弱的广义凸性假定下讨论多目标规划的几种整体有效性．给出的定理统一了目前已有的一些关于多目标规划局部解为整体解的充分条件．     

非光滑半无限多目标优化问题的最优性充分条件

研究了一个非光滑半无限多目标优化问题(简记为SIMOP),并讨论了它的最优性条件.首先, 通过对目标函数和约束函数的某种组合赋予Clarke F-凸性假设, 获得了SIMOP(弱)有效解的最优性充分条件.接下来, 用Chankong-Haimes方法建立了此SIMOP的一个标量问题并得到了这个标量问题的最优性充分条件.     

多目标最优化G-恰当有效解集的存在性和连通性

本文证明了非空紧凸集上拟凸多目标最优化问题的G-恰当有效解的存在性．在此基础上，得到了向量目标函数既是似凸又是拟凸的多目标最优化问题的G-恰当有效解集是连通的结论．同时，还给出一个关于Pareto有效解集连通性的新结果．     

On sufficiency and duality in multiobjective programming problem under generalized <Emphasis Type="Italic">α</Emphasis>-type I univexity

In this paper, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized α-univex type I vector valued functions. A number of Kuhn–Tucker type sufficient optimality conditions are obtained for a feasible solution to be an efficient solution. The Mond–Weir type duality results are also presented.     

Generalized convexity and efficiency for non-regular multiobjective programming problems with inequality-type constraints

For multiobjective problems with inequality-type constraints the necessary conditions for efficient solutions are presented. These conditions are applied when the constraints do not necessarily satisfy any regularity assumptions, and they are based on the concept of 2-regularity introduced by Izmailov. In general, the necessary optimality conditions are not sufficient and the efficient solution set is not the same as the Karush-Kuhn-Tucker points set. So it is necessary to introduce generalized convexity notions. In the multiobjective non-regular case we give the notion of 2-KKT-pseudoinvex-II problems. This new concept of generalized convexity is both necessary and sufficient to guarantee the characterization of all efficient solutions based on the optimality conditions.