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

作者：Ceng, Lu-Chuan; Guu, Sy-Ming^*; Yao, Jen-Chih

来源：Journal of Global Optimization, 2014, 60(4): 617-634.

DOI：10.1007/s10898-013-0087-5

• Extragradient method
• Mann-type CQ method
• Hybrid gradient projection algorithm with regularization
• Minimization problem
• Asymptotically strict pseudocontractive mapping in the intermediate sense

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.

• 出版日期2014-12
• 单位上海大学; 上海师范大学; 长春大学