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Strong Convergence of Modified Algorithms Based on the Regularization for the Constrained Convex Minimization Problem

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  • Ming Tian
  • Jun-Ying Gong

Abstract

As is known, the regularization method plays an important role in solving constrained convex minimization problems. Based on the idea of regularization, implicit and explicit iterative algorithms are proposed in this paper and the sequences generated by the algorithms can converge strongly to a solution of the constrained convex minimization problem, which also solves a certain variational inequality. As an application, we also apply the algorithm to solve the split feasibility problem.

Suggested Citation

  • Ming Tian & Jun-Ying Gong, 2014. "Strong Convergence of Modified Algorithms Based on the Regularization for the Constrained Convex Minimization Problem," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:870102
    DOI: 10.1155/2014/870102
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    References listed on IDEAS

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    1. A. E. Al-Mazrooei & A. Latif & J. C. Yao, 2014. "Solving Generalized Mixed Equilibria, Variational Inequalities, and Constrained Convex Minimization," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. L. C. Ceng & A. Petruşel & J. C. Yao, 2013. "Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-25, March.
    3. L. C. Ceng & A. Petruşel & J. C. Yao, 2013. "Relaxed Extragradient Methods with Regularization for General System of Variational Inequalities with Constraints of Split Feasibility and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. 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.
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