A strongly convergent modification of the proximal point algorithm in nonsmooth Banach spaces


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	A strongly convergent modification of the proximal point algorithm in nonsmooth Banach spaces


	Fixed Point Theory, Volume 19, No. 1, 2018, 107-122, February 1st, 2018 DOI: 10.24193/fpt-ro.2018.1.09 Authors: Souhail Chebbi, Najla Altwaijry and Hong-Kun Xu Abstract: Rockafellar's proximal point algorithm is known to be not strongly convergent in general in an infinite-dimensional Hilbert space. Effort has thus been made to modify this algorithm so that strong convergence is guaranteed. In this paper we provide a strongly convergent modification of Rockafellar's proximal point algorithm in a uniformly convex Banach space which is not necessarily smooth. Key Words and Phrases: Maximal monotone operator, proximal point algorithm, strong convergence, generalized projection, uniformly convex Banach space, zero point. 2010 Mathematics Subject Classification: 90C25, 47H05, 90C30, 46B20, 47H09. Published on-line: February 1st, 2018. Abstract pdf Fulltext pdf Back to volume's table of contents