Strong stability implies Mangasarian–Fromovitz Constraint Qualification

Abstract

In 1980, M. Kojima introduced the topological concept of strongly stable stationary solutions in smooth nonlinear optimization. In case that the Mangasarian–Fromovitz Constraint Qualification (MFCQ) is satisfied, he characterized strong stability with the aid of first- and second-order derivatives of the objective function and the constraint functions. In this article, we show that the MFCQ is, in fact, implied by the assumption of strong stability.

†Dedicated to Diethard Pallaschke on the occasion of his 65th birthday.

Keywords:

• Nonlinear optimization
• Strong stability
• Mangasarian–Fromovitz Constraint qualification

Keywords:

• AMS Classification: 90C31

Notes

†Dedicated to Diethard Pallaschke on the occasion of his 65th birthday.