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

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  • Lu-Chuan Ceng
  • Sy-Ming Guu
  • Jen-Chih Yao

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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Lu-Chuan Ceng & Sy-Ming Guu & Jen-Chih Yao, 2014. "Hybrid methods with regularization for minimization problems and asymptotically strict pseudocontractive mappings in the intermediate sense," Journal of Global Optimization, Springer, vol. 60(4), pages 617-634, December.
    • Handle: RePEc:spr:jglopt:v:60:y:2014:i:4:p:617-634
    DOI: 10.1007/s10898-013-0087-5
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    References listed on IDEAS

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    1. Hong-Kun Xu, 2011. "Averaged Mappings and the Gradient-Projection Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 360-378, August.
    2. Ceng, Lu-Chuan & Yao, Jen-Chih, 2007. "Approximate proximal methods in vector optimization," European Journal of Operational Research, Elsevier, vol. 183(1), pages 1-19, November.
    3. L. C. Ceng & A. Petruşel & J. C. Yao, 2009. "Iterative Approaches to Solving Equilibrium Problems and Fixed Point Problems of Infinitely Many Nonexpansive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 37-58, October.
    4. Lu-Chuan Ceng & Nicolas Hadjisavvas & Ngai-Ching Wong, 2010. "Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems," Journal of Global Optimization, Springer, vol. 46(4), pages 635-646, April.
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