This chapter is devoted to recent developments of vector and set optimization. Based on the concept of a pre-order optimal elements are defined. In vector optimization properties of optimal elements and existence results are gained. Further, an introduction to vector optimization with a variable...

For many practical applications it is important to determine not only a numerical approximation of one but a representation of the whole set of globally optimal solutions of a non-convex optimization problem. Then one element of this representation may be chosen based on additional information...

In this paper, we study a method for finding robust solutions to multiobjective optimization problems under uncertainty. We follow the set-based minmax approach for handling the uncertainties which leads to a certain set optimization problem with the strict upper type set relation. We introduce,...

This book presents adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarization approaches. Readers will benefit from the new adaptive methods and ideas for solving multiobjective optimization.

1 Variable ordering structures -- 2 Optimality concepts and their characterization -- 3 Properties of cone-valued maps -- 4 Linear scalarizations -- 5 Nonlinear scalarizations -- 6 Scalarization for variable orderings given by Bishop-Phelps cones -- 7 Optimality conditions -- 8 Duality results...