Bilevel Vector Pseudomonotone Equilibrium Problems: Duality and Existence∗
نویسندگان
چکیده
The aim of this paper is devoted to investigate the duality and existence of solutions for a class of bilevel vector pseudomonotone equilibrium problems without involving the information about the solution set of the lower-level equilibrium problem. Firstly, we propose the dual formulations of bilevel vector equilibrium problems (BVEP). Secondly, the primal-dual relationships are derived under cone-convexity and weak pseudo-monotonicity assumptions. Finally, the existence of solutions of BVEP are established without involving the information about the solution set of the lower-level problem.
منابع مشابه
On Penalty and Gap Function Methods for Bilevel Equilibrium Problems
We consider bilevel pseudomonotone equilibrium problems. We use a penalty function to convert a bilevel problem into one-level ones. We generalize a pseudo-∇-monotonicity concept from ∇monotonicity and prove that under pseudo-∇-monotonicity property any stationary point of a regularized gap function is a solution of the penalized equilibrium problem. As an application, we discuss a special case...
متن کاملDuality for vector equilibrium problems with constraints
In the paper, we study duality for vector equilibrium problems using a concept of generalized convexity in dealing with the quasi-relative interior. Then, their applications to optimality conditions for quasi-relative efficient solutions are obtained. Our results are extensions of several existing ones in the literature when the ordering cones in both the objective space and the constr...
متن کاملSaddle Point Problems, Bilevel Problems, and Mathematical Program with Equilibrium Constraint on Complete Metric Spaces
We apply an existence theorem of variational inclusion problem on metric spaces to study optimization problems, set-valued vector saddle point problems, bilevel problems, and mathematical programs with equilibrium constraint on metric spaces. We study these problems without any convexity and compactness assumptions. Our results are different from any existence results of these types of problems...
متن کاملSome existence results for generalized vector quasi-equilibrium problems
In this paper, we introduce and study a class of generalized vector quasi-equilibrium problem, which includes many vector equilibrium problems, equilibrium problems, vector variational inequalities and variational inequalities as special cases. Using one person game theorems, the concept of escaping sequences and without convexity assumptions, we prove some existence results for ...
متن کاملOn Equilibrium Problems Involving Strongly Pseudomonotone Bifunctions
We study equilibrium problems with strongly pseudomonotone bifunctions in real Hilbert spaces. We show the existence of a unique solution. We then propose a generalized strongly convergent projection method for equilibrium problems with strongly pseudomonotone bifunctions. The proposed method uses only one projection without requiring Lipschitz continuity. Application to variational inequalitie...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014