A Vectorization Scheme for Nonconvex Set Optimization Problems

In this paper, we study a solution approach for set optimization problems with respect to the lower set less relation. This approach can serve as a base for numerically solving set optimization problems by using established solvers from multiobjective optimization. Our strategy consists of deriving a parametric family of multiobjective optimization problems whose optimal solution … Read more

A Steepest Descent Method for Set Optimization Problems with Set-Valued Mappings of Finite Cardinality

In this paper, we study a first-order solution method for a particular class of set optimization problems where the solution concept is given by the set approach. We consider the case in which the set-valued objective mapping is identified by a finite number of continuously differentiable selections. The corresponding set optimization problem is then equivalent … Read more

The Fermat Rule for Set Optimization Problems with Lipschitzian Set-Valued Mappings

n this paper, we consider set optimization problems with respect to the set approach. Specifically, we deal with the lower less and the upper less set relations. First, we derive properties of convexity and Lipschitzianity of suitable scalarizing functionals, under the same assumption on the set-valued objective mapping. We then obtain upper estimates of the … Read more

A Unified Characterization of Nonlinear Scalarizing Functionals in Optimization

Over the years, several classes of scalarization techniques in optimization have been introduced and employed in deriving separation theorems, optimality conditions and algorithms. In this paper, we study the relationships between some of those classes in the sense of inclusion. We focus on three types of scalarizing functionals (by Hiriart-Urruty, Drummond and Svaiter, Gerstewitz) and … Read more