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21.
讨论Stampacchia集值广义向量拟均衡问题,利用数值化方法,在适当的条件下得出其解的存在性定理,这些定理推广和统一了近期类似问题的一些结果. 相似文献
22.
讨论Stampacchia广义向量拟均衡问题,利用数值化方法,在适当的单调性和连续性条件下得出解的存在性定理。 相似文献
23.
R. J. Gallagher 《Journal of Optimization Theory and Applications》1995,84(3):665-674
In 1953 Arrow, Barankin, and Blackwell proved that, ifR
n
is equipped with its natural ordering and ifF is a closed convex subset ofR
n
, then the set of points inF that can be supported by strictly positive linear functionals is dense in the set of all efficient (maximal) points ofF. Many generalizations of this density result to infinite-dimensional settings have been given. In this note, we consider the particular setting where the setF is contained in the topological dualY
* of a partially ordered, nonreflexive normed spaceY, and the support functionals are restricted to be either nonnegative or strictly positive elements in the canonical embedding ofY inY
*. Three alternative density results are obtained, two of which generalize a space-specific result due to Majumdar for the dual system (Y,Y
*)=(L
1,L
).This research was supported in part by funds provided by the Provident Chair of Excellence in Applied Mathematics at the University of Tennessee, Chattanooga, Tennessee. 相似文献
24.
W. B. Gearhart 《Journal of Optimization Theory and Applications》1989,62(2):321-332
LetF be a family of real-valued maps onR
n, and letY be a subset ofR
n. Denote byS(Y|F) the set of ally* Y such that, for somef F,f(y)f(y*) for ally inY. Let us say thatF is a scalarization family if, for any subsetY,S(Y|F) is equal to the set of properly efficient points inY. General conditions forF to be a scalarization family were given in Ref. 1. However, scalarization families must contain nondifferentiable functions. In this note, it is shown that, if the condition of Ref. 1 which forces nondifferentiability is dropped, thenS(Y|F) is dense in the set of properly efficient points. 相似文献
25.
F. Ferro 《Journal of Optimization Theory and Applications》1993,79(1):127-138
We deal with the problem of scalarization in vector optimization. A very general form of the Arrow-Barankin-Blackwell theorem is proved in normed spaces. We study the question also in the spacel
of all bounded sequences of real numbers, which is of particular interest in economic problems, and generalize many of the existing results on this subject. 相似文献
26.
周轩伟 《高校应用数学学报(A辑)》2008,23(3)
利用n维Euclid空间中较多锥的闭包,定义了多目标规划强较多有效解.利用较多锥闭包的Minkowski泛函,给出了强较多有效解和弱较多有效解的标量化结果,并讨论了强较多有效解和弱较多有效解的标量对偶问题及其应用. 相似文献
27.
On Ekeland's Variational Principle for Set-Valued Mappings 总被引:1,自引:0,他引:1
Sheng-jie Li Wen-yan Zhang College of Mathematics Science Chongqing University Chongqing China 《应用数学学报(英文版)》2007,(1)
In this paper,we derive a general vector Ekeland variational principle for set-valued mappings,which has a closed relation to εk~O-efficient points of set-valued optimization problems.The main result presentedin this paper is a generalization of the corresponding result in[3]. 相似文献
28.
Gap functions for a system of generalized vector quasi-equilibrium problems with set-valued mappings
In this paper, some gap functions for three classes of a system of generalized vector quasi-equilibrium problems with set-valued
mappings (for short, SGVQEP) are investigated by virtue of the nonlinear scalarization function of Chen, Yang and Yu. Three
examples are then provided to demonstrate these gap functions. Also, some gap functions for three classes of generalized finite
dimensional vector equilibrium problems (GFVEP) are derived without using the nonlinear scalarization function method. Furthermore,
a set-valued function is obtained as a gap function for one of (GFVEP) under certain assumptions.
相似文献
29.
Peter I. Kogut 《Applicable analysis》2013,92(5):994-1009
We study vector optimization problems in partially ordered Banach spaces and suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We discuss the so-called adaptive scalarization of such problems and show that the corresponding scalar non-linear optimization problems can be by-turn approximated by quadratic minimization problems. 相似文献
30.
Joë l Benoist Jonathan M. Borwein Nicolae Popovici 《Proceedings of the American Mathematical Society》2003,131(4):1109-1113
The aim of this paper is to characterize in terms of scalar quasiconvexity the vector-valued functions which are -quasiconvex with respect to a closed convex cone in a Banach space. Our main result extends a well-known characterization of -quasiconvexity by means of extreme directions of the polar cone of , obtained by Dinh The Luc in the particular case when is a polyhedral cone generated by exactly linearly independent vectors in the Euclidean space .