Uncertain Vector Optimization Problems: Duality and Optimality

Uncertain vector optimization is one of the frontier subjects in the fields of optimization theory and applications. This project aims to deeply study duality, optimality conditions and related applications of uncertain vector optimization problems by using image space analysis and robust optimization methods. We mainly intend to focus on the following aspects: By using image space analysis and separation functions, we intend to establish unified dual models for uncertain vector optimization problems with fixed or variable partial orders structures, to discuss their basic properties such as zero duality gap between primal problem and its dual problem. We intend to propose some new relax robust optimization methods and some new approaches to reformulating uncertain vector optimization problems into tractable fixed optimization problems and uncertain optimization problems, and to introduce some new constraint qualifications and conceptions of robust solutions by the image space analysis, variational analysis and various set order relations. Also, we intend to establish new theorems of alternative and optimality conditions for various robust solutions of uncertain vector optimization problems via separation functions.