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Hybrid methods with regularization for minimization problems and asymptotically strict pseudocontractive mappings in the intermediate sense

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Abstract

In this paper we introduce an iterative algorithm for finding a common element of the fixed point set of an asymptotically strict pseudocontractive mapping S in the intermediate sense and the solution set of the minimization problem (MP) for a convex and continuously Frechet differentiable functional in Hilbert space. The iterative algorithm is based on several well-known methods including the extragradient method, CQ method, Mann-type iterative method and hybrid gradient projection algorithm with regularization. We obtain a strong convergence theorem for three sequences generated by our iterative algorithm. In addition, we also prove a new weak convergence theorem by a modified extragradient method with regularization for the MP and the mapping S.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Lu-Chuan Ceng

  2. Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, 200234, China

    Lu-Chuan Ceng

  3. Graduate Institute of Business and Management, College of Management, Chang Gung University, Kwei Shan, Taoyuan Hsien, Taiwan

    Sy-Ming Guu

  4. Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung, 807, Taiwan

    Jen-Chih Yao

  5. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jidda, Saudi Arabia

    Jen-Chih Yao

Authors
  1. Lu-Chuan Ceng
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  2. Sy-Ming Guu
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  3. Jen-Chih Yao
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Correspondence to Sy-Ming Guu.

Additional information

This research was partially supported by the National Science Foundation of China (11071169), Innovation Program of Shanghai Municipal Education Commission (09ZZ133) and Leading Academic Discipline Project of Shanghai Normal University (DZL707). This research was partially supported by NSC 100-2221-E-182-072-MY2. This research was partially supported by the grant NSC 99-2115-M-037-002-MY3.

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Ceng, LC., Guu, SM. & Yao, JC. Hybrid methods with regularization for minimization problems and asymptotically strict pseudocontractive mappings in the intermediate sense. J Glob Optim 60, 617–634 (2014). https://doi.org/10.1007/s10898-013-0087-5

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  • DOI: https://doi.org/10.1007/s10898-013-0087-5

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