Maximilian Volk – Optimization Online

Generalized polarity and weakest constraint qualifications in multiobjective optimization

Published: 2022/09/06

Multi-Criteria Optimization generalized bipolar cone, Generalized polar cone, multiobjective Kuhn-Tucker condition, multiobjective stationarity condition, weakest constraint qualification

In G. Haeser, A. Ramos, Constraint Qualifications for Karush-Kuhn-Tucker Conditions in Multiobjective Optimization, JOTA, Vol.~187 (2020), 469-487, a generalization of the normal cone from single objective to multiobjective optimization is introduced, along with a weakest constraint qualification such that any local weak Pareto optimal point is a weak Kuhn-Tucker point. We extend this approach to … Read more

On the weakest constraint qualification for sharp local minimizers

Published: 2022/06/23, Updated: 2023/03/10

Oliver Stein

Maximilian Volk

Constrained Nonlinear Optimization cardinality constraint, Guignard constraint qualification, strict local minimizer of order one, Strong local minimizer, weakest constraint qualification

The sharp local minimality of feasible points of nonlinear optimization problems is known to possess a characterization by a strengthened version of the Karush-Kuhn-Tucker conditions, as long as the Mangasarian-Fromovitz constraint qualification holds. This strengthened condition is not easy to check algorithmically since it involves the topological interior of some set. In this paper we … Read more