On strong second-order necessary optimality conditions under relaxed constant rank constraint qualification

Abstract

We discuss the (first- and second-order) optimality conditions for nonlinear programming under the relaxed constant rank constraint qualification (RCRCQ). Although the optimality conditions are well established in the literature, the proofs presented here are based solely on the well-known inverse function theorem. This is the only prerequisite from real analysis used to establish two auxiliary results needed to prove the optimality conditions. To be precise, we provide a simple and alternative proof that RCRCQ is a constraint qualification that implies strong second-order optimality conditions.

Keywords:

• Nonlinear programming
• second-order optimality conditions
• constraint qualifications
• relaxed constant rank constraint qualification

Acknowledgments

We are thankful to the remarks and suggestions of the reviewers, which helped us to improve the presentation of this work.

Disclosure statement

No potential conflict of interest was reported by the author(s).