Lower semicontinuity of solution mapping to parametric generalized strong vector equilibrium problems

In this paper, the lower semicontinuity of solution mapping to parametric generalized strong vector equilibrium problems without the assumptions of monotonicity and compactness is established by using a new proof method which is different from the ones used in the literature.     

Continuity of the solution mappings to parametric generalized strong vector equilibrium problems

In this paper, we establish the upper semicontinuity and lower semicontinuity of solution mappings to a parametric generalized strong vector equilibrium problem with setvalued mappings by using a scalarization method and a density result. The results improve the corresponding ones in the literature. Some examples are given to illustrate our results.     

Semicontinuity of the solution set to a parametric generalized strong vector equilibrium problem

This paper deals with the stability for a parametric generalized strong vector equilibrium problem. Under new assumptions, which do not contain any information about the solution set and monotonicity, we establish the lower semicontinuity and upper semicontinuity of the solution set to a parametric generalized strong vector equilibrium problem by using a scalarization method and a density result. These results are improve the corresponding ones in recent literature. Some examples are given to illustrate our results.     

Continuity of the solution mappings to parametric generalized vector equilibrium problems

The aim of this paper is to establish the continuity of the efficient solution mappings to a parametric generalized strong vector equilibrium problem, by using the Hölder relation. Our result extends and improves some recent results in the references therein.     

Solution semicontinuity of parametric generalized vector equilibrium problems

In this paper, the lower semicontinuity and continuity of the solution mapping to a parametric generalized vector equilibrium problem involving set-valued mappings are established by using a new proof method which is different from the ones used in the literature.     

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.     

Upper semicontinuity result for the solution mapping of a mixed parametric generalized vector quasiequilibrium problem with moving cones

In this paper, we give sufficient conditions for the upper semicontinuity property of the solution mapping of a parametric generalized vector quasiequilibrium problem with mixed relations and moving cones. The main result is proven under the assumption that moving cones have local openness/local closedness properties and set-valued maps are cone-semicontinuous in a sense weaker than the usual sense of semicontinuity. The nonemptiness and the compactness of the solution set are also investigated.     

Continuity of the solution mapping to parametric generalized vector equilibrium problems

In this paper, two kinds of parametric generalized vector equilibrium problems in normed spaces are studied. The sufficient conditions for the continuity of the solution mappings to the two kinds of parametric generalized vector equilibrium problems are established under suitable conditions. The results presented in this paper extend and improve some main results in Chen and Gong (Pac J Optim 3:511–520, 2010), Chen and Li (Pac J Optim 6:141–152, 2010), Chen et al. (J Glob Optim 45:309–318, 2009), Cheng and Zhu (J Glob Optim 32:543–550, 2005), Gong (J Optim Theory Appl 139:35–46, 2008), Li and Fang (J Optim Theory Appl 147:507–515, 2010), Li et al. (Bull Aust Math Soc 81:85–95, 2010) and Peng et al. (J Optim Theory Appl 152(1):256–264, 2011).     

A note on the lower semicontinuity of efficient solutions for parametric vector equilibrium problems

By using a new assumption, the lower semicontinuity of the efficient solution mappings for parametric vector equilibrium problems without a monotonicity assumption is established. Our result is different from recent ones in the literature. Some examples are given to illustrate the case.     

On the lower semicontinuity of the set of efficient solutions to parametric generalized systems

In this paper, we investigate weak vector solutions and global vector solutions to a parametric generalized system (PGS). By using a weaker assumption, we discuss the lower semicontinuity of solution maps for PGS under the case that the $f$ -efficient solution mapping may not be single-valued. These results extend the recent ones in the literature. Some examples are given to illustrate our results.     

Lower semicontinuity of the solution map to a parametric vector variational inequality

This paper is concerned with the study of solution stability of a parametric vector variational inequality, where mappings may not be strongly monotone. Under some requirements that the operator of a unperturbed problem is monotone or it satisfies degree conditions then we show that the solution map of a parametric vector variational inequality is lower semicontinuous.     

On a generalized vector equilibrium problem with bounds

We prove the existence of a solution to the generalized vector equilibrium problem with bounds. We show that several known theorems from the literature can be considered as particular cases of our results, and we provide examples of applications related to best approximations in normed spaces and variational inequalities.     

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.     

On the lower semicontinuity of optimal solution sets

We study the lower semicontinuity of the optimal solution set of a parametric optimization problem. Our results sharpen the main results of Zhao (1997, The lower semicontinuity of optimal solution sets. Journal of Mathematical Analysis and Applications, 207, 240–254. Ref. ). Namely, it is shown that the conclusion of Theorem 1 of is still valid under weaker assumptions, and the conditions on “ε-nontriviality” and uniform continuity of the objective function in Theorems 2 and 3 of can be omitted.     

On the parametric linear complementarity problem: A generalized solution procedure

This paper presents a solution procedure for the parametric linear complementarity problemIw–Mz=q+sp,w ^T z=0,w0, andz0, whereM is a positive semidefinite matrix or aP-matrix. This procedure is different from existing ones in the way it handles initialization. By exploiting special relationships between the vectorsq andp, it can reduce computational effort. Sinceq is an arbitrary vector, the procedure can be used for the ordinary linear complementarity problem. In that case, it produces pivots exactly analogous to those of Lemke's algorithm.This paper is based on the author's doctoral dissertation at Johns Hopkins University, 1977. The author wishes to thank her advisors, Professors C. S. ReVelle and D. J. Elzinga. During the last year of her graduate studies, the author held an AAUW-IBM dissertation fellowship.     

Lower semicontinuity of the solution map to a parametric elliptic optimal control problem with mixed pointwise constraints

This paper studies the solution stability of a parametric optimal control problem governed by single linear elliptic equations with mixed control-state constraints and convex cost functions. By reducing the problem to a parametric programming problem and a parametric variational inequality, we obtain sufficient conditions under which the solution map to an elliptic optimal control problem is lower semicontinuous.     

On the generalized vector equilibrium problems

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.