Parametric Optimization with a Bottleneck Objective and Vector Optimization

Abstract

In this paper, efficient and weakly efficient points of a set are characterized by an optimization problem with a parameter in the bottleneck objective function. The investigation of the structure of the parameter set leads to a necessary and sufficient criterion for the non-emptiness of the set of efficient points. The continuous dependence of the optimization problem on the parameter is investigated. Finally, the results are applied to a scalarization of multi-objective optimization problems.