Generalized penalization and maximization of vectorial nonsmooth functions

Abstract

We use directional Lipschitz concepts and a minimal time function with respect to a set of directions in order to derive generalized penalization results for Pareto minimality in set-valued constrained optimization. Then, we obtain necessary optimality conditions for maximization in constrained vector optimization in terms of generalized differentiation objects. To the latter aim, we deduce first some enhanced calculus rules for coderivatives of the difference of two mappings. All the main results of this paper are tailored to model directional features of the optimization problem under study.

Keywords:

• Vector optimization
• penalization
• subdifferential calculus
• maximization

Acknowledgements

The authors thank the anonymous reviewer for helpful remarks.

Notes

No potential conflict of interest was reported by the authors.

Dedicated to Professor Franco Giannessi on the occasion of his 80th birthday and to Professor Diethard Pallaschke on the occasion of his 75th birthday.

Additional information

Funding

This research was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI [project number PN-II-RU-TE-2014-4-0019].