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Solving Generalized Mixed Equilibria, Variational Inequalities, and Constrained Convex Minimization

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  • A. E. Al-Mazrooei
  • A. Latif
  • J. C. Yao

Abstract

We propose implicit and explicit iterative algorithms for finding a common element of the set of solutions of the minimization problem for a convex and continuously Fréchet differentiable functional, the set of solutions of a finite family of generalized mixed equilibrium problems, and the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings in a real Hilbert space. We prove that the sequences generated by the proposed algorithms converge strongly to a common element of three sets, which is the unique solution of a variational inequality defined over the intersection of three sets under very mild conditions.

Suggested Citation

  • A. E. Al-Mazrooei & A. Latif & J. C. Yao, 2014. "Solving Generalized Mixed Equilibria, Variational Inequalities, and Constrained Convex Minimization," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-26, January.
    • Handle: RePEc:hin:jnlaaa:587865
    DOI: 10.1155/2014/587865
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