On uniqueness of Kuhn-Tucker multipliers in nonlinear programming

Abstract

Recently Fujiwara, Han and Mangasarian introduced a new constraint qualification which is a slight tightening of the well-known Mangasarian—Fromovitz constraint qualification. We show that this new qualification is a necessary and sufficient condition for the uniqueness of Kuhn—Tucker multipliers. We also show that it implies the satisfaction of second order necessary optimality conditions at a local minimum.