joint work with Truong Q. Bao
In this talk, we are dealing with necessary conditions for minimal solutions of constrained and unconstrained optimization problems with respect to general domination sets by using well-known nonlinear scalarization functionals with uniform level sets. The primary objective of this work is to establish revised formulas for basic and singular subdifferentials of the nonlinear scalarization functionals.The second objective is to propose a new way to scalarize a set-valued optimization problem.
This paper is concerned with a certain historical background on set relations and scalarization methods for sets. Based on a basic idea of sublinear scalarization in vector optimization, we introduce a scalarization scheme for sets in a real vector space such that each scalarizing function has an order-monotone property for set relation and inherited properties on cone-convexity and cone-continuity. Accordingly, we show a certain application for this idea to establish some kinds of set-valued inequalities. Moreover, we shall mention another application to fuzzy theory.
joint work with Radu Strugariu
In this talk, we consider some barrier methods for vector optimization problems with geometric and generalized inequality constraints. Firstly, we investigate some constraint qualification conditions and we compare them to the corresponding ones in literature, and then we introduce some barrier functions and we prove several of their basic properties in fairly general situations. Finally, we derive convergence results of the associated barrier method, and to this aim we restrict ourselves to convex case and finite dimensional setting.