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Nonlinear Programming via König’s Maximum Theorem

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Abstract

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.

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Acknowledgments

The authors would like to thank the referees for their helpful suggestions. Research partially supported by Junta de Andalucía Grant FQM359.

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  1. University of Granada, Granada, Spain

    P. Montiel López & M. Ruiz Galán

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  1. P. Montiel López
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  2. M. Ruiz Galán
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Correspondence to M. Ruiz Galán.

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Montiel López, P., Ruiz Galán, M. Nonlinear Programming via König’s Maximum Theorem. J Optim Theory Appl 170, 838–852 (2016). https://doi.org/10.1007/s10957-016-0959-1

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