Nonlinear Programming via Konig's Maximum Theorem

作者：Montiel Lopez P; Ruiz Galan M

来源：Journal of Optimization Theory and Applications, 2016, 170(3): 838-852.

DOI：10.1007/s10957-016-0959-1

• Nonlinear programming
• Hahn-Banach theorem
• Separation theorem
• Lagrange multipliers
• Karush/Kuhn-Tucker theorem
• Fritz John theorem
• Infsup-convexity

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 Konig'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.

• 出版日期2016-9