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1.
In this paper, we study a weak generalized Ky Fan inequality with cone constraints through image space analysis. First, we characterize the separation for the weak generalized Ky Fan inequality with cone constraints using the saddle points of generalized Lagrangian function. Then, we use regular weak separation functions to construct gap functions and regularized gap functions for the weak generalized Ky Fan inequality with cone constraints in a general way, and establish its error bounds in terms of these gap functions.  相似文献   

2.
We establish the following theorems: (i) an existence theorem for weak type generalized saddle points; (ii) an existence theorem for strong type generalized saddle points; (iii) a generalized minimax theorem for a vector-valued function. These theorems are generalizations and extensions of the author's recent results. For such extensions, we propose new concepts of convexity and continuity of vector-valued functions, which are weaker than ordinary ones. Some of the proofs are based on a few key observations and also on the Browder coincidence theorem or the Tychonoff fixed-point theorem. Also, the minimax theorem follows from the existence theorem for weak type generalized saddle points. The main spaces with mathematical structures considered are real locally convex spaces and real ordered topological vector spaces.This paper is dedicated to Professor Kensuke Tanaka on his sixtieth birthday.This paper was written when the author was a visitor at the Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Niigata, Japan. The author is indebted to Prof. K. Tanaka for suggesting this work.The author is very grateful to Prof. P. L. Yu for his useful encouragement and suggestions and to the referees for their valuable suggestions and comments.  相似文献   

3.
Generalized Semicontinuity and Existence Theorems for Cone Saddle Points   总被引:11,自引:0,他引:11  
This paper is concerned with existence theorems for generalized saddle points (cone saddle points) of vector-valued functions. A concept of lower semicontinuity for vector-valued functions is introduced and its properties are investigated. Previous results of the author are extended by using the lower semicontinuity. Accepted 26 April 1996  相似文献   

4.
广义次似凸集值优化的鞍点定理   总被引:1,自引:1,他引:0  
讨论广义次似凸集值优化的鞍点定理.给出广义次似凸集值映射的两个性质.定义广义次似凸集值优化的Fritz-John鞍点和Kuhn-Tucker鞍点.获得一系列广义次似凸集值优化的鞍点定理.  相似文献   

5.
向量映射的鞍点和Lagrange对偶问题   总被引:4,自引:0,他引:4  
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。  相似文献   

6.
In this paper, we develop the sufficient conditions for the existence of local and global saddle points of two classes of augmented Lagrangian functions for nonconvex optimization problem with both equality and inequality constraints, which improve the corresponding results in available papers. The main feature of our sufficient condition for the existence of global saddle points is that we do not need the uniqueness of the optimal solution. Furthermore, we show that the existence of global saddle points is a necessary and sufficient condition for the exact penalty representation in the framework of augmented Lagrangians. Based on these, we convert a class of generalized semi-infinite programming problems into standard semi-infinite programming problems via augmented Lagrangians. Some new first-order optimality conditions are also discussed. This research was supported by the National Natural Science Foundation of P.R. China (Grant No. 10571106 and No. 10701047).  相似文献   

7.
In this paper, Stampacchia generalized vector quasiequilibrium problem and generalized vector loose saddle points for set-valued mappings are introduced. By using the scalarization method and the fixed-point theorem, existence theorems are established.This work was supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jiangxi Province, China. The author is grateful to Professor F. Giannessi and the referee for valuable comments and careful reading improving the original draft.Communicated by F. Giannessi  相似文献   

8.
《Optimization》2012,61(1):73-91
In this paper we consider mainly vector optimization problems under generalized cone-convexlikeness and generalized cone-subconvexlikeness in real linear spaces having or not topology. We establish the adapted definitions to wide frame of real linear spaces, and we show the characterizations for several concepts of generalized convexity and the relationships among them. From separation theorems, some characterizations of efficiency and weak efficiency are given in terms of scalarization. A new extension of Gordan-form alternative theorem is given here, and derived from it, we obtain optimality conditions by means of linear operators rules and saddle point criterions.  相似文献   

9.
广义度量S-KKM映射的性质及其对鞍点问题的应用   总被引:3,自引:0,他引:3  
引入了S为集盥映射情况下的广义度量S-KKM映射和超S-γ-广义拟凸(凹)函数,建立了广义度量S-KKM映射原理和广义度量S-KKM映射与超S-γ-广义拟凸(凹)函数的关系.作为应用,获得了超凸度量空间中的新的Ky Fan极大极小不等式和鞍点定理.  相似文献   

10.
For inequality constrained optimization problem, we show the existence of local saddle point of generalized augmented Lagrangian under weak second-order sufficient conditions which are weaker than the second-order sufficient conditions in the literature. We further discuss the existence of global saddle points without requiring the uniqueness of the global optimal solution. This work was supported by the National Natural Science Foundation of China grants 10571106, 10471159.  相似文献   

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