共查询到20条相似文献,搜索用时 15 毫秒
1.
I. V. Konnov 《Russian Mathematics (Iz VUZ)》2012,56(9):5-13
We consider scalarization issues for vector problems in the case where the preference relation is represented by a rather arbitrary set. An algorithm for weights choice for a priori unknown preference relations is suggested. Some examples of applications to vector optimization, game equilibrium, and variational inequalities are described. 相似文献
2.
This paper investigates some properties of approximate efficiency in variable ordering structures where the variable ordering structure is given by a special set valued map. We characterize -minimal and - nondominated elements as approximate solutions of a multiobjective optimization problem with a variable ordering structure and give necessary and sufficient conditions for these solutions, via scalarization. 相似文献
3.
Weak vector equilibrium problems with bi-variable mappings from product space of two bounded complete locally convex Hausdorff topological vector spaces to another topological vector space are studied. The existence theorems of solutions are proved by the FKKM fixed point theorem. Viscosity principle of vector equilibrium problems is dealt with. The relations between solutions of the vector equilibrium problem and those of its perturbation problem are presented. 相似文献
4.
This paper presents a global optimization approach for solving signomial geometric programming (SGP) problems. We employ an accelerated extended cutting plane (ECP) approach integrated with piecewise linear (PWL) approximations to solve the global optimization of SGP problems. In this approach, we separate the feasible regions determined by the constraints into convex and nonconvex ones in the logarithmic domain. In the nonconvex feasible regions, the corresponding constraint functions are converted into mixed integer linear constraints using PWL approximations, while the other constraints with convex feasible regions are handled by the ECP method. We also use pre-processed initial cuts and batched cuts to accelerate the proposed algorithm. Numerical results show that the proposed approach can solve the global optimization of SGP problems efficiently and effectively. 相似文献
5.
The conventional equilibrium problem found in many economics and network models is based on a scalar cost, or a single objective. Recently, equilibrium problems based on a vector cost, or multicriteria, have received considerable attention. In this paper, we study a scalarization method for analyzing network equilibrium problems with vector-valued cost function. The method is based on a strictly monotone function originally proposed by Gerstewitz. Conditions that are both necessary and sufficient for weak vector equilibrium are derived, with the prominent feature that no convexity assumptions are needed, in contrast to other existing scalarization methods. 相似文献
6.
In this paper, by using a weaker assumption, we discuss the Hölder continuity of solution maps for two cases of parametric generalized vector equilibrium problems under the case that the solution map is a general set-valued one, but not a single-valued one. These results extend the recent ones in the literature. Several examples are given for the illustration of our results. 相似文献
7.
Necessary optimality conditions for efficient solutions of unconstrained and vector equilibrium problems with equality and inequality constraints are derived. Under assumptions on generalized convexity, necessary optimality conditions for efficient solutions become sufficient optimality conditions. Note that it is not required here that the ordering cone in the objective space has a nonempty interior. 相似文献
8.
Yu Han 《Optimization》2016,65(2):357-367
In this paper, we establish the connectedness of the sets of Henig efficient solutions, globally efficient solutions, weak efficient solutions, superefficient solutions and efficient solutions for a class of generalized vector equilibrium problems without the assumptions of monotonicity and compactness. 相似文献
9.
We consider parametric multivalued vector equilibrium problems of both weak and strong types in metric linear spaces. Sufficient conditions for the local uniqueness and Hölder continuity of the solutions are established. As consequences some new results for variational inequalities are derived and compared with recent papers on the subject. 相似文献
10.
利用Gertewitz泛函研究向量优化问题的一类非线性标量化问题. 证明了向量优化问题的(C, \varepsilon)-弱有效解或(C, \varepsilon)-有效解与标量化问题的近似解或严格近似解间的等价关系, 并估计了标量化问题的近似解. 相似文献
11.
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
12.
In this paper, a generalized vector equilibrium problem is introduced and studied. A scalar characterization of weak efficient
solutions for the generalized vector equilibrium problem is obtained. By using the scalarization result, the existence of
the weak efficient solutions and the connectedness of the set of weak efficient solutions for the generalized vector equilibrium
problem are proved in locally convex spaces. 相似文献
13.
M. Durea 《Journal of Mathematical Analysis and Applications》2007,333(2):1165-1179
In this paper we consider several concepts of approximate minima of a set in normed vector spaces and we provide some results concerning the stability of these minima under perturbation of the underlying set with a sequence of sets converging in the sense of Painlevé-Kuratowski to the initial set. Then, we introduce the concept of approximate solution for equilibrium problem governed by set-valued maps and we study the stability of these solutions. The particular case of linear continuous operators is considered as well. 相似文献
14.
In this paper, a generalized vector equilibrium problem with set-valued maps defined on a reflexive Banach space is considered. By using the recession method, we first give the conditions under which the solution set is non-empty, convex and weakly compact, and then extend it to the strong generalized vector equilibrium problem. This facilitates generalizing and modifying various existence theorems. Furthermore, the topological properties of the solution set are studied and it is shown that the solution set includes some boundary points. 相似文献
15.
A.P. Farajzadeh A. Amini-Harandi 《Journal of Mathematical Analysis and Applications》2008,344(2):999-1004
In this paper, generalized vector equilibrium problems are studied and some existence theorems of solutions for these problems in the setting of topological vector spaces are proved. Sufficient conditions for the set of solutions to be compact and convex are given. Our results improve some recent results in this field. 相似文献
16.
利用G\"{o}pfert等提出的非线性标量化函数给出了向量优化中\varepsilon-真有效解的一个非线性标量化性质, 并提出几个例子对主要结果进行了解释. 相似文献
17.
This work concerns with vector equilibrium problems where the image space of the bifunction is not endowed with any topology. To be precise, a kind of “semi-algebraic” upper semicontinuity notion is introduced and, by means of a recent algebraic version of the so-called Gerstewitz’s functional, a new existence result of weak efficient solutions is obtained that significantly improves some previous ones stated in the topological setting since it requires weaker assumptions. 相似文献
18.
Adela Capătă 《Journal of Global Optimization》2011,51(4):657-675
In this paper, we present sufficient conditions for the existence of Henig efficient solutions, superefficient solutions and
Henig globally efficient solutions of a vector equilibrium problem in topological vector spaces, using a well-known separation
theorem in infinite dimensional spaces. As an application, using a scalarization technique, existence results for proper efficient
solutions of generalized vector variational inequalities are given. 相似文献
19.
In this paper, we study the generalized vector equilibrium problems in real Hausdorff topological vector space settings. The concepts of weak solutions and strong solutions are introduced. Several new results of existence for the weak solutions and strong solutions of generalized vector equilibrium problems are derived. The new results extend and modify various existence theorems for similar problems. 相似文献
20.
We introduce and study two notions of well-posedness for vector equilibrium problems in topological vector spaces; they arise
from the well-posedness concepts previously introduced by the same authors in the scalar case, and provide an extension of
similar definitions for vector optimization problems. The first notion is linked to the behaviour of suitable maximizing sequences,
while the second one is defined in terms of Hausdorff convergence of the map of approximate solutions. In this paper we compare
them, and, in a concave setting, we give sufficient conditions on the data in order to guarantee well-posedness. Our results
extend similar results established for vector optimization problems known in the literature.
相似文献