William Karush and the KKT Theorem Richard

This chapter is mainly about William Karush and his role in the Karush-KuhnTucker theorem of nonlinear programming. It tells the story of fundamental optimization results that he obtained in his master’s thesis: results that he neither published nor advertised and that were later independently rediscovered and published by Harold W. Kuhn and Albert W. Tucker. The principal result – which concerns necessary conditions of optimality in the problem of minimizing a function of several variables constrained by inequalities – first became known as the Kuhn–Tucker theorem. Years later, when awareness of Karush’s pioneering work spread, his name was adjoined to the name of the theorem where it remains to this day. Still, the recognition of Karush’s discovery of this key result left two questions unanswered: why was the thesis not published? and why did he remain silent on the priority issue? After learning of the thesis work, Harold Kuhn wrote to Karush stating his intention to set the record straight on the matter of priority, and he did so soon thereafter. In his letter to Karush, Kuhn posed these two questions, and Karush answered them in his reply. These two letters are quoted below. Although there had long been optimization problems calling for the maximization or minimization of functions of several variables subject to constraints, it took the advent of linear programming to inspire the name “nonlinear programming.” This term was first used as the title of a paper [30] by Harold W. Kuhn and Albert W. Tucker. Appearing in 1951, the paper contained many results, but interest focused on the one declaring conditions that must be satisfied by a solution of the