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Generic uniqueness theorems with some applications

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  • Dingtao Peng
  • Jian Yu
  • Naihua Xiu

Abstract

We first present a proper condition under which the image of a set-valued mapping becomes a singleton and then obtain several generic uniqueness theorems which can be applied to study the uniqueness of the solutions for nonlinear problems. As applications, we prove that, in the sense of Baire category, most optimization problems (respectively, saddle point problems and variational inequality problems) have unique solution. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Dingtao Peng & Jian Yu & Naihua Xiu, 2013. "Generic uniqueness theorems with some applications," Journal of Global Optimization, Springer, vol. 56(2), pages 713-725, June.
    • Handle: RePEc:spr:jglopt:v:56:y:2013:i:2:p:713-725
    DOI: 10.1007/s10898-012-9903-6
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    References listed on IDEAS

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    1. Alexander J. Zaslavski, 2010. "Optimization on Metric and Normed Spaces," Springer Optimization and Its Applications, Springer, number 978-0-387-88621-3, June.
    2. Monica Bianchi & Siegfried Schaible, 2004. "Equilibrium Problems under Generalized Convexity and Generalized Monotonicity," Journal of Global Optimization, Springer, vol. 30(2), pages 121-134, November.
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