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An Extremum Principle for Smooth Problems

Author

Listed:
  • Dariusz Idczak

    (Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland)

  • Stanisław Walczak

    (Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland
    Faculty of Mathematics and Computer Science, Stefan Batory State University, Batorego 64C, 96-100 Skierniewice, Poland)

Abstract

We derive an extremum principle. It can be treated as an intermediate result between the celebrated smooth-convex extremum principle due to Ioffe and Tikhomirov and the Dubovitskii–Milyutin theorem. The proof of this principle is based on a simple generalization of the Fermat’s theorem, the smooth-convex extremum principle and the local implicit function theorem. An integro-differential example illustrating the new principle is presented.

Suggested Citation

  • Dariusz Idczak & Stanisław Walczak, 2020. "An Extremum Principle for Smooth Problems," Games, MDPI, vol. 11(4), pages 1-6, November.
    • Handle: RePEc:gam:jgames:v:11:y:2020:i:4:p:56-:d:451943
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    Citations

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    Cited by:

    1. Ellina Grigorieva, 2021. "Optimal Control Theory: Introduction to the Special Issue," Games, MDPI, vol. 12(1), pages 1-4, March.

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