Majid Soleimani-damaneh: Vector Optimization utilizing mathematical analysis tools: Some theory and application

In this talk, we deal with the vector optimization problems in finite and infinite dimensional vector spaces. Different solution concepts are discussed and some applications of vector optimization in Biology, Economics, and Banking are addressed briefly. Some difficulties in defining the solution concepts for vector optimization problems are mentioned. To overcome these difficulties, one has to use some algebraic concepts (e.g. (relative) algebraic interior or vectorial closure) or define approximate solutions instead of the exact ones. The main aim of this presentation is surveying some recent advances in solving these problems. Furthermore, we talk about nonsmooth optimization in Banach spaces briefly. Developments in this field provide new connections between functional analysis, vector optimization and convex analysis.