Saddle-Point Optimality Criteria of Nonlinear Programming Problems over Cones without Differentiability
Vince A. Sposito, H. T. David · SIAM Journal on Applied Mathematics · 1971
This paper considers Kuhn–Tucker duality without differentiability conditions for the types of domains recently treated in the literature in which the two orthants of the classical Kuhn–Tucker theory are replaced by a convex cone L and a set C that is typically, but not necessarily, convex. A natural modification of the Slater condition, in addition to the convexity of a certain auxiliary set, yields sufficiency of the constrained optimization problem for the associated saddle-point problem. No conditions are required for the converse.