Nonlinear Programming via König’s Maximum Theorem - Montiel Lopez, P; Ruiz Galan, M (Journal of optimization theory and applications, 2016)
Starting from one extension of the Hahn–Banach theorem, the Mazur–Orlicz theorem, and a not very restrictive concept of convexity, that arises naturally in minimax theory, infsup-convexity, we derive an equivalent version of that fundamental result for finite dimensional spaces, which is a sharp generalization of König’s Maximum theorem. It implies several optimal statements of the Lagrange multipliers, Karush/Kuhn–Tucker, and Fritz John type for nonlinear programs with an objective function subject to both equality and inequality constraints.