Research Projects

Set-valued optimization is a rapidly growing area of research, with a focus on the set-relation approach. Initially, vector approaches were prominent, but the set-relation approach has become more natural and appealing. The author's doctoral studies have focused on the existence of solutions, well-posedness, and robustness of set-valued optimization problems in the set-relation approach. The proposal aims to extend research in set-valued optimization problems, particularly in bilevel programming, set-valued measure of risk, and studying regret robustness. Bilevel programming is an interesting area that can model real-life decision problems, with two levels: lower level and upper level. The author proposes establishing a set-valued explanation of bilevel programming, especially for multi-objective bilevel programming problems. Robust optimization is another growing area of research, with the author introducing regret robustness, a popular concept in management sciences, and extending it to multi-objective optimization problems. The second aim is to extend the idea of regret robustness for set-valued optimization problems. The measure of risk is another important notion in the financial community, and a connection between risk and robust optimization has been explored in the literature. A set-valued coherent measure of risk has also been introduced recently. However, the connection between set-valued measure of risk and set-valued robust optimization problems has not been studied yet.