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1.
Theorems of the Alternative and Optimization with Set-Valued Maps   总被引:16,自引:0,他引:16  
In this paper, the concept of generalized cone subconvexlike set-valued mapsis presented and a theorem of alternative for the system of generalizedinequality–equality set-valued maps is established. By applying thetheorem of the alternative and other results, necessary and sufficientoptimality conditions for vector optimization problems with generalizedcone subconvexlike set-valued maps are obtained.  相似文献
2.
Under generalized cone-subconvexlikeness for vector-valued mappings in locally-convex Hausdorff topological vector spaces, a Gordan-form alternative theorem is derived. Some characterizations of the Benson proper efficiency under this generalized convexity are established in terms of scalarization, Lagrangian multipliers, saddle-point criterion, and duality.  相似文献
3.
A vector variational inequality and optimization over an efficient set   总被引:7,自引:0,他引:7  
Some relations are obtained between weak vector minimization, a vector variational inequality, and the optimization of a utility function over a set of efficient points.
Zusammenfassung Es werden einige Beziehungen über schwache Vektorminimierung, einer vektoriellen Variationsgleichung und der Optimierung einer Nutzenfunktion über einer Menge effizienter Punkte hergeleitet.
  相似文献
4.
On the Stability of Generalized Vector Quasivariational Inequality Problems   总被引:4,自引:0,他引:4  
In this paper, we obtain some stability results for generalized vector quasivariational inequality problems. We prove that the solution set is a closed set and establish the upper semicontinuity property of the solution set for perturbed generalized vector quasivariational inequality problems. These results extend those obtained in Ref. 1. We obtain also the lower semicontinuity property of the solution set for perturbed classical variational inequalities. Several examples are given for the illustration of our results.  相似文献
5.
Vector network equilibrium problems and nonlinear scalarization methods   总被引:3,自引:0,他引:3  
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.
A vector variational inequality is studied. The paper deals with existence theorems for solutions under convexity assumptions and without convexity assumptions.This research was partially supported by the Italian Research Council (CNR), Group for Functional Analysis and Applications (GNAFA), and was carried out while the author was Visiting Professor at the Department of Mathematics, University of Pisa, September–November, 1989.  相似文献
7.
8.
Generalized Arrow-Barankin-Blackwell theorems in locally convex spaces   总被引:2,自引:0,他引:2  
This paper deals with generalizations of the Arrow-Barankin-Blackwell theorem in locally convex spaces, partially ordered by cones whose duals have nonempty quasi-interiors.This research has been partially supported by the World Laboratory, Lausanne, Switzerland, by the Department of Mathematics, University of Pisa, Pisa, Italy, and by the National Natural Sciences Foundation of China. Useful discussions with Professor F. Ferro are gratefully acknowledged.  相似文献
9.
Minimax Theorems for Set-Valued Mappings   总被引:1,自引:0,他引:1  
In this paper, we deal with two types of minimax theorems for set-valued mappings and vector-valued functions.  相似文献
10.
Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. In this paper we introduce a nonlinear scalarization function for a variable domination structure. Several important properties, such as subadditiveness and continuity, of this nonlinear scalarization function are established. This nonlinear scalarization function is applied to study the existence of solutions for generalized quasi-vector equilibrium problems. This paper is dedicated to Professor Franco Giannessi for his 68th birthday  相似文献
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