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Superimposed optimization methods for the mixed equilibrium problem and variational inclusion

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  • Yonghong Yao
  • Yeong-Cheng Liou
  • Ngai-Ching Wong

Abstract

The purpose of this paper is to construct two superimposed optimization methods for solving the mixed equilibrium problem and variational inclusion. We show that the proposed superimposed methods converge strongly to a solution of some optimization problem. Note that our methods do not involve any projection. Copyright Springer Science+Business Media, LLC. 2013

Suggested Citation

  • Yonghong Yao & Yeong-Cheng Liou & Ngai-Ching Wong, 2013. "Superimposed optimization methods for the mixed equilibrium problem and variational inclusion," Journal of Global Optimization, Springer, vol. 57(3), pages 935-950, November.
    • Handle: RePEc:spr:jglopt:v:57:y:2013:i:3:p:935-950
    DOI: 10.1007/s10898-012-9982-4
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    References listed on IDEAS

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    1. O. Chadli & N.C. Wong & J.C. Yao, 2003. "Equilibrium Problems with Applications to Eigenvalue Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 245-266, May.
    2. Yao, Yonghong & Cho, Yeol Je & Liou, Yeong-Cheng, 2011. "Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems," European Journal of Operational Research, Elsevier, vol. 212(2), pages 242-250, July.
    3. S. Takahashi & W. Takahashi & M. Toyoda, 2010. "Strong Convergence Theorems for Maximal Monotone Operators with Nonlinear Mappings in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(1), pages 27-41, October.
    4. I. V. Konnov & S. Schaible & J. C. Yao, 2005. "Combined Relaxation Method for Mixed Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 309-322, August.
    5. N. Nadezhkina & W. Takahashi, 2006. "Weak Convergence Theorem by an Extragradient Method for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 191-201, January.
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