Nonlinear Programming via König’s Maximum Theorem

• Published in: Journal of optimization theory and applications Vol. 170; no. 3; pp. 838 - 852
• Main Authors: Montiel Lopez, P, Ruiz Galan, M
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2016; Springer Nature B.V
• Subjects: Applications of Mathematics; Banach spaces; Calculus of Variations and Optimal Control; Optimization; Engineering; Equivalence; Inequalities; Inequality; Lagrange multiplier; Lagrange multipliers; Mathematical analysis; Mathematics; Mathematics and Statistics; Minimax technique; Nonlinear programming; Operations Research/Decision Theory; Optimization; Studies; Theorems; Theory of Computation; Vector space; 90C30; Fritz John theorem; 90C46; Lagrange multipliers; Karush/Kuhn–Tucker theorem; 46A22; Nonlinear programming; 26B25; Separation theorem; Infsup-convexity; Hahn–Banach theorem

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 gen...