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 eta and the Lagrange multiplier gamma 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. (C) 1999 Academic Press.