On a theorem due to Crouzeix and Ferland

摘要

In this article we introduce the notions of Kuhn-Tucker and Fritz John pseudoconvex nonlinear programming problems with inequality constraints. We derive several properties of these problems. We prove that the problem with quasiconvex data is (second-order) Kuhn-Tucker pseudoconvex if and only if every (second-order) Kuhn-Tucker stationary point is a global minimizer. We obtain respective results for Fritz John pseudo-convex problems. For the first-order case we consider Frechet differentiable functions and locally Lipschitz ones, for the second-order case Frechet and twice directionally differentiable functions.