Introduction

Linear programming aroused interest in constraints in the form of inequalities and in the theory of linear inequalities and convex sets. The study of Kuhn-Tucker (Kuhn was a student of Tucker and became the principal investigator, worked together on several projects dealing with linear and nonlinear programming problems under generous sponsorship of the Naval Research from 1948 until 1972) appeared in the middle of this interest with a full recognition of such developments.

Kuhn–Tucker (1951) first used the name “Nonlinear Programming.” However, the theory of nonlinear programming when the constraints are all in the form of equalities has been known for a long time. The inequality constraints were treated in a fairly satisfactory manner by Karush (1939) in his M.Sc. thesis, at the Department of Mathematics, University of Chicago. A summary of the thesis was published as an appendix to: Kuhn (1976). Karush’s work is apparently under the influence of a similar work in the calculus of variations by Valentine (1937). As a struggling graduate student meeting requirements for going on to his Ph.D., the thought of publication never occurred to Karush and he was not encouraged to publish his Master’s thesis by his supervisor L.M. Graves. At that time, no one anticipated the future interest in these problems and their potential practical applications. The school of classical calculus of variations at Chicago also popularized the theory of optimal control under the name of the “Pontryagin’s maximum principle.”