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A Generalized Variational Principle and Its Application to Equilibrium Problems

Author

Listed:
  • Csaba Farkas

    (Babeş-Bolyai University)

  • Andrea Éva Molnár

    (Babeş-Bolyai University)

Abstract

In this paper, we prove a generalized Ekeland-type variational principle for bifunctions, by showing the existence of solution for some generalized optimization problems. In a particular case, from this result, we obtain a Zhong-type variational principle for bifunctions, which may be important from algorithmic point of view, because the solution can be localized in a sphere. Contrary to the standard literature, we are able to guarantee the existence of solution without assuming the triangle property.

Suggested Citation

  • Csaba Farkas & Andrea Éva Molnár, 2013. "A Generalized Variational Principle and Its Application to Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 156(2), pages 213-231, February.
    • Handle: RePEc:spr:joptap:v:156:y:2013:i:2:d:10.1007_s10957-012-0101-y
    DOI: 10.1007/s10957-012-0101-y
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    References listed on IDEAS

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    1. Q. H. Ansari & S. Schaible & J. C. Yao, 2000. "System of Vector Equilibrium Problems and Its Applications," Journal of Optimization Theory and Applications, Springer, vol. 107(3), pages 547-557, December.
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