Minimizing the difference of two quasiconvex functions over a vector-valued quasiconvex system

Abstract

The article is concerned with an optimization problem $\left(P\right)$ where we minimize the difference of two quasiconvex scalar functions under a vector-valued quasiconvex system. Using the Q-subdifferential introduced by Suzuki and Kuroiwa [Optimality conditions and the basic constraint qualification for quasiconvex programming. Nonlinear Anal. 2011;74:1279–1285], together with a special constraint qualification, we give necessary optimality conditions to $\left(P\right).$

Keywords:

• Basic constraint qualification
• quasiconvex functions
• generators
• extreme directions
• Q-subdifferentials

2010 Mathematics Subject Classifications:

• Primary 90C26
• 90C46
• Secondary 49K99

Acknowledgments

Our sincere acknowledgements to the anonymous referees for their insightful remarks and suggestions. The second author has been supported by the Alexander von Humboldt-foundation.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Stephan Dempe  http://orcid.org/0000-0001-6344-5152