Approaches to set optimization without convexity assumptions [article]

Elisabeth Köbis, Baasansuren Jadamba, Boris S. Morduchovič, Christiane Tammer, Martin-Luther Universität, Universitäts- Und Landesbibliothek Sachsen-Anhalt
This work is concerned with providing solution concepts and methods for solving set optimization problems without convexity assumptions. A special focus is put on set relations, as these are crucial ingredients in the so-called set approach. Generalized set relations are introduced and characterized by means of nonlinear functionals. In addition, variable domination structures as well as approximate solution concepts are introduced and studied. For these concepts, solution procedures by means
more » ... ocedures by means of generalized Jahn-Graef-Younes methods and derivative-free descent methods are provided, tested and verified. As an application of set optimization, uncertain vector-valued optimization problems are investigated.
doi:10.25673/35671 fatcat:vxjucjl7andn7ngsigxoq4zhuq