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0-Epi families of mappings, topological degree, and optimization

Abstract

Using the concept of 0-epi mapping defined by Furi, Martelli, and Vignoli, we define the concept of 0-epi family of quasiconvex mappings. We prove that the theory of 0-epi families is a good substitute of the degree theory in the localization of Nash equilibrium points, because it is more refined and very simple.

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Communicated by G. Leitmann

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Isac, G. 0-Epi families of mappings, topological degree, and optimization. J Optim Theory Appl 42, 51–75 (1984). https://doi.org/10.1007/BF00934133

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Key Words

  • Nash equilibrium points
  • 0-epi mappings
  • topological degree
  • quasiconvex mappings
  • quasisubgradient