Parametric Vector Equilibrium Problems Research Articles

Sensitivity analysis of parametric weak vector equilibrium problems

In this paper, two implicit multifunction theorems are obtained. Then by using a set-valued gap function and the results obtained we study the sensitivity analysis of the solution mapping for a parametric weak vector equilibrium problem and obtain an explicit expression for the contingent derivative of the solution mapping.

Continuity of approximate solution mappings for parametric equilibrium problems

In this paper, we obtain sufficient conditions for Hausdorff continuity and Berge continuity of an approximate solution mapping for a parametric scalar equilibrium problem. By using a scalarization method, we also discuss the Berge lower semicontinuity and Berge continuity of a approximate solution mapping for a parametric vector equilibrium problem.

A Note on Hölder Continuity of Solution Set for Parametric Vector Quasiequilibrium Problems

By using a scalarization technique, we extend and sharpen the results in S. Li and X. Li (2011) on the Hölder continuity of the solution sets of parametric vector equilibrium problems to the case of parametric vector quasiequilibrium problems in metric spaces. Furthermore, we also give an example to illustrate that our main results are applicable.

Closedness of the solution map for parametric weak vector equilibrium problems

In this paper we introduced a new definition of vector topological pseudomonotonicity to study the parametric weak vector equilibrium problems. The main result gives sufficient conditions for closedness of the solution map defined on the set of parameters.

Closedness and Hadamard well-posedness of the solution map for parametric vector equilibrium problems

In this paper we introduced new definitions of vector topological pseudomonotonicity to study the parametric vector equilibrium problems. The main result gives sufficient conditions for closedness of the solution map defined on the set of parameters. The Hadamard well-posedness of parametric vector equilibrium problems is also analyzed by using the new definitions of vector topological pseudomonotonicity.

A new proof approach to lower semicontinuity for parametric vector equilibrium problems

In this note, the lower semicontinuity of the set of efficient solutions to generalized systems is established by using a new proof method which is different from the one used in Gong (J Optim Theory Appl 138:197–205, 2008). Our result improve his corresponding one.

SENSITIVITY ANALYSIS OF VECTOR EQUILIBRIUM PROBLEMS

In this paper, we introduce a type of parametric vector equilibrium problem on topological vector spaces. This problem includes parametric vector variational inequality problem and ε-vector equilibrium problem and so on, as special cases. Existence and some continuity properties for the of solution mapping of the parametric vector equilibrium problem are established.

Continuity of the Solution Set to Parametric Weak Vector Equilibrium Problems

In this paper, we obtain some stability results for parametric weak vector equilibrium problems in topological vector spaces. We provide sufficient conditions for the continuity of the solution set mapping in parametric weak monotone vector equilibrium problems.

Well-posedness for parametric vector equilibrium problems with applications

In this paper, we study the parametric well-posedness for vector equilibrium problems and propose a generalized well-posed concept for equilibrium problems with equilibrium constraints (EPEC in short) in topological vector spaces setting. We show that under suitable conditions, the well-posedness defined by approximating solution nets is equivalent to the upper semicontinuity of the solution mapping of perturbed problems. Further, since optimization problems and variational inequality problems are special cases of equilibrium problems, related variational problems can be adopted under some equivalent conditions. Finally, we also study the relationship between well-posedness and parametric well-posedness.

Sensitivity for parametric vector equilibria

In this article, we consider a parametric vector equilibrium problem in topological vector spaces, or metric spaces, if needed, defined as follows: given , find such that where the order in Y is defined by a suitable fixed cone C. We study the upper stability of the map of the solutions S=S(λ), providing results in the peculiar framework of generalized monotone functions. In the particular case of a single-valued solution map, we provide conditions for the Hölder regularity of S in both cases when K is fixed, and also when it depends on a parameter.

Stability for parametric implicit vector equilibrium problems

In this paper, we consider a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces where a mapping f and a set K are perturbed by parameters ϵ and λ , respectively. We establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution set mapping S : Λ 1 × Λ 2 → 2 X for such parametric implicit vector equilibrium problems.

On the Hölder continuity of solutions to parametric multivalued vector equilibrium problems

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.