共查询到20条相似文献,搜索用时 31 毫秒
1.
H. Huang 《Journal of Mathematical Analysis and Applications》2008,342(1):503-513
In this paper, we study constrained multiobjective optimization problems with objectives being closed-graph multifunctions in Banach spaces. In terms of the coderivatives and Clarke's normal cones, we establish Lagrange multiplier rules for super efficiency as necessary or sufficient optimality conditions of the above problems. 相似文献
2.
《Applied Mathematics Letters》2003,16(4):453-458
We prove an existence result for strong solutions of an implicit vector variational inequality with multifunctions by following the approach of Theorem 3.1 in [1]. The aim of this paper is to extend Theorem 3.1 in [1] to the multifunction case with moving cones. 相似文献
3.
Using variational analysis, we study the vector optimization problems with objectives being closed multifunctions on Banach spaces or in Asplund spaces. In terms of the coderivatives and normal cones, we present Fermat’s rules as necessary or sufficient conditions for a super efficient solution of the above problems. 相似文献
4.
Xi-Yin Zheng 《数学研究》2016,49(4):379-392
Metric subregularity is an important and active area in modern variational
analysis and nonsmooth optimization. Many existing results on the metric subregularity
were established in terms of coderivatives of the multifunctions concerned. This
note tries to give a survey of the metric subregularity theory related to the coderivatives
and normal cones. 相似文献
5.
Issoufou Kouada 《Mathematical Methods of Operations Research》1997,46(2):169-192
Following a few words on multifunctions in the mathematical literature, a very brief recall on dual spaces, some preliminary notations and definitions in the introduction, we give some results on those functions in the second paragraph. In the third paragraph, a duality theory in cone-optimization involving multifunctions is developed with the concept of the strong instead of the weak cone-optimality criterium. The results so obtained account for existing ones on univocal vector-function optimization and they hold in spaces of arbitrary dimension.The author is grateful to the refuree's helpful suggestions. 相似文献
6.
Using variational analysis, we study vector optimization problems with objectives being closed multifunctions on Banach spaces or in Asplund spaces. In particular, in terms of the coderivatives, we present Fermat’s rules as necessary conditions for an optimal solution of the above problems. As applications, we also provide some necessary conditions (in terms of Clarke’s normal cones or the limiting normal cones) for Pareto efficient points.This research was supported by a postdoctoral fellowship scheme (CUHK) and an Earmarked Grant from the Research Grant Council of Hong Kong. Research of the first author was also supported by the National Natural Science Foundation of P. R. China (Grant No. 10361008) and the Natural Science Foundation of Yunnan Province, P. R. China (Grant No. 2003A002M). 相似文献
7.
Dušan Holý 《Mathematica Slovaca》2007,57(6):561-570
We study spaces of multifunctions with closed values, multifunctions with closed graphs, USCO multifunctions, minimal USCO
multifunctions and the space of densely continuous forms as metric spaces, equipped with the topology of uniform convergence.
We give conditions under which these metric spaces are complete.
相似文献
8.
S. Gautier 《Numerical Functional Analysis & Optimization》2013,34(7-8):679-699
In this paper, we want to compare two classes of multifunctions which can be used as approximating multifunctions in differentiability theory: affine and eclipsing multifunctions. We show how the notion of eclipsing multifunctions is an extension of affine multifunctions, and what kinds of difficulties arise in this extension. 相似文献
9.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):157-179
This paper proposes an approximation approach to the solution of chance-constrained stochastic programming problems. The results rely in a fundamental way on the theory of convergence of sequences of measurable multifunctions. Particular results are presented for stochastic linear programming problems. 相似文献
10.
Huynh Van Ngai Nguyen Huu Tron Michel Théra 《Journal of Optimization Theory and Applications》2014,160(2):355-390
The metric regularity of multifunctions plays a crucial role in modern variational analysis and optimization. This property is a key to study the stability of solutions of generalized equations. Many practical problems lead to generalized equations associated to the sum of multifunctions. This paper is devoted to study the metric regularity of the sum of multifunctions. As the sum of closed multifunctions is not necessarily closed, almost all known results in the literature on the metric regularity for one multifunction (which is assumed usually to be closed) fail to imply regularity properties of the sum of multifunctions. To avoid this difficulty, we use an approach based on the metric regularity of so-called epigraphical multifunctions and the theory of error bounds to study the metric regularity of the sum of two multifunctions, as well as some related important properties of variational systems. Firstly, we establish the metric regularity of the sum of a regular multifunction and a pseudo-Lipschitz multifunction with a suitable Lipschitz modulus. These results subsume some recent results by Durea and Strugariu. Secondly, we derive coderivative characterizations of the metric regularity of epigraphical multifunctions associated with the sum of multifunctions. Applications to the study of the behavior of solutions of variational systems are reported. 相似文献
11.
Evgeny A. Poletsky 《Arkiv f?r Matematik》2004,42(2):335-352
This paper describes plurisubharmonic convexity and hulls, and also analytic multifunctions in terms of Jensen measures. In
particular, this allows us to get a new proof of Słodkowski's theorem stating that multifunctions are analytic if and only
if their graphs are pseudoconcave. We also show that multifunctions with plurisubharmonically convex fibers are analytic if
and only if their graphs locally belong to plurisubharmonic hulls of their boundaries. In the last section we prove that minimal
analytic multifunctions satisfy the maximum principle and give a criterion for the existence of holomorphic selections in
the graphs of analytic multifunctions.
The author was partially supported by an NSF Grant. 相似文献
12.
In this paper, the upper and lower δ-continuous multifunctions in fuzzy setting have been presented as a strong form and an application of fuzzy continuous multifunctions. Certain characterizations and several properties of these fuzzy multifunctions along with their mutual relationships are obtained. Attempts are also made to correlate this new class with the corresponding known types of fuzzy multifunctions. Also, applicability of the above new concepts to superstrings and
space time could be probably possible in the near future. 相似文献
13.
《Chaos, solitons, and fractals》2001,12(13):2387-2394
In this paper, we introduce and study γ-continuous multifunctions as a generalization of quasi-continuous multifunctions due to Popa in 1985 and precontinuous multifunctions due to Popa in 1988. Some characterizations and several properties concerning upper (lower) γ-continuous multifunctions are obtained. The relationships between upper (lower) γ-continuous multifunctions and some known concepts are also discussed. 相似文献
14.
In this paper we study the area minimizing problem in some kinds of conformal cones. This concept is a generalization of the cones in Euclidean spaces and the cylinders in product manifolds. We define a non-closed-minimal (NCM) condition for bounded domains. Under this assumption and other necessary conditions we establish the existence of bounded minimal graphs in mean convex conformal cones. Moreover those minimal graphs are the solutions to corresponding area minimizing problems. We can solve the area minimizing problem in non-mean convex translating conformal cones if these cones are contained in a larger mean convex conformal cones with the NCM assumption. We give examples to illustrate that this assumption can not be removed for our main results. 相似文献
15.
In this paper we introduce and study δ-precontinuous multifunctions as a generalization of precontinuous multifunctions due to Popa [Problemy Mat. 10 (1988) 9]. Some characterizations and several properties concerning upper (lower) δ-precontinuous multifunctions are obtained. The relationships between upper (lower) δ-precontinuous multifunctions and some known concepts are also discussed. 相似文献
16.
This article is devoted to the study of stability conditions for a class of quasi-equilibrium problems with variable cones in normed spaces. We introduce concepts of upper and lower semicontinuity of vector-valued mappings involving variable cones and their properties, we also propose a key hypothesis. Employing this hypothesis and such concepts, we investigate sufficient/necessary conditions of the Hausdorff semicontinuity/continuity for solution mappings to such problems. We also discuss characterizations for the hypothesis which do not contain information regarding solution sets. As an application, we consider the special case of traffic network problems. Our results are new or improve the existing ones. 相似文献
17.
黄辉 《高校应用数学学报(A辑)》2007,22(1):74-80
考虑了伪凸集值映射的误差界.证明了对于伪凸集值映射,局部误差界成立意味着整体误差界成立.通过相依导数,给出了伪凸集值映射存在误差界的一些等价叙述. 相似文献
18.
On Some Almost-Periodicity Problems in Various Metrics 总被引:1,自引:0,他引:1
The Bohr-type and the Bochner-type definitions for almost periodic functions are examined in various metrics (Stepanov, Weyl and Besicovitch). The correct definitions of Besicovitch-like multifunctions are given. Weak almost-periodic solutions are proved for differential equations and inclusions. This problem is also discussed as a fixed-point problem in function spaces. 相似文献
19.
In this work, we introduce and study a class of generalized vector equilibrium problems for multifunctions which includes a number of generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. By using the KKM–Fan theorem and Nadler’s result, we prove an existence theorem for solutions for this class of generalized vector equilibrium problems in Banach spaces. Applications to generalized vector variational-like inequalities are given. 相似文献
20.
In this paper, some vector optimization problems are considered where pseudo-ordering relations are determined by nonconvex
cones in Banach spaces. We give some characterizations of solution sets for vector complementarity problems and vector variational
inequalities. When the nonconvex cone is the union of some convex cones, it is shown that the solution set of these problems
is either an intersection or an union of the solution sets of all subproblems corresponding to each of these convex cones
depending on whether these problems are defined by the nonconvex cone itself or its complement. Moreover, some relations of
vector complementarity problems, vector variational inequalities, and minimal element problems are also given.
While this paper was being revised in September 2006, Professor Alex Rubinov (the second author of the paper) left us due
to the illness. This is a very sad news to us. We dedicate this paper to the memory of Professor Rubinov as a mathematician
and truly friend. 相似文献