KKT and Fritz-John Optimality Conditions for Constrained Optimization

April K. Andreas, Engineering and Mathematics, McLennan Community College

Optimality conditions for Fritz-John and Karush Kuhn Tucker (KKT) points provide a reasonably-straightforward strategy for solving nonlinear optimization problems. In fact, KKT conditions are necessary, if not sufficient, for proving optimality. In this article, we introduce Fritz-John and KKT optimality conditions for constrained optimization. We begin by reviewing some essential definitions for completing the logic, including Gordon’s and Farkas’ Lemmas. We derive the Fritz-John conditions and show when these conditions are necessary to show optimality. We then derive the necessary and sufficient KKT conditions for optimality. The article concludes with two simple numerical examples illustrating Fritz-John and KKT theory.

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