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 η 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.