A new constraint qualification and a second-order necessary optimality condition for mathematical programming problems

Abstract

We present a new condition of constraint qualification that involves a second-order tangent set. Based on this constraint qualification, we establish a second-order necessary optimality condition for mathematical programming problems. The new qualification condition is weaker than the popular constraint qualification of Robinson. An example is presented to show the usefulness of the result. The results can be applied to problems with abstract feasible sets as well as to problems with feasible regions defined explicitly by nonconvex equalities and inequalities. © Yokohama Publishers.