Invexity and the Kuhn]Tucker Theorem

It is pointed out that Type 1 invex functions are the most general class of functions relevant to necessary and sufficient conditions for Kuhn]Tucker optimality in nonlinear programming. Linear programming duality is used to show an equivalence between the concept of invexity and the Kuhn]Tucker conditions for optimality. The invexity kernel h and the Lagrange multiplier y in the Kuhn]Tucker theory are dual variables. The Kuhn]Tucker conditions are necessary conditions for optimality provided that certain constraint qualifications apply. A particular result given here is that invexity in itself constitutes an appropriate constraint qualification