In this article we develop a new approach to duality theory for convex vector optimization problems. We modify a given (set-valued) vector optimization problem such that the image space becomes a complete lattice (a sublattice of the power set of the original image space), where the corresponding infimum and supremum are sets that are related to the set of (minimal and maximal) weakly efficient...

We introduce a new type of the system of generalized strong vector quasiequilibrium problems with set-valued mappings in real locally convex Hausdorff topological vector spaces. We establish an existence theorem by using Kakutani-Fan-Glicksberg fixed-point theorem and discuss the closedness of strong solution set for the system of generalized strong vector quasiequilibrium problem. The results ...

A fading-memory system is a system that tends to forget its input asymptotically over time. It has been shown that discrete-time fading-memory systems can be uniformly approximated arbitrarily closely over a set of bounded input sequences simply by uniformly approximating sufficiently closely either the external or internal representation of the system. In other words, the problem of uniformly ...

We discuss new applications of advanced tools of variational analysis and generalized differentiation to a number of important problems in optimization theory, equilibria, optimal control, and feedback control design. The presented results are largely based on the recent work by the author and his collaborators. Among the main topics considered and briefly surveyed in this paper are new calculu...

Throughout this paper, we use intA and CoA to denote the interior and the convex hull of a set A, respectively. Let I be an index set. For each i ∈ I , let Yi, Ei be two Hausdorff topological vector spaces. Consider a family of nonempty convex subsets {Xi}i∈I with Xi ⊆ Ei. Let X = ∏ i∈I Xi and E = ∏ i∈I Ei. An element of the set Xi = ∏ j∈I\i Xi will be denoted by xi; therefore, x ∈ X will be wr...

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 ...

We consider a multi-step algorithm to approximate a common element of the set of solutions of monotone and Lipschitz-type continuous equilibrium problems, and the set of common fixed points of a finite family of set-valued mappings satisfying condition (E). We prove strong convergence theorems of such an iterative scheme in real Hilbert spaces. This common solution is the unique solution of a v...