Strong convergence of a proximal-type algorithm in a Banach space

摘要

In this paper, we study strong convergence of the proximal point algorithm. It is known that the proximal point algorithm converges weakly to a solution of a maximal monotone operator, but it fails to converge strongly. Then, in [Math. Program., 87 (2000), pp. 189 202], Solodov and Svaiter introduced the new proximal-type algorithm to generate a strongly convergent sequence and established a convergence property for it in Hilbert spaces. Our purpose is to extend Solodov and Svaiter's result to more general Banach spaces. Using this, we consider the problem of finding a minimizer of a convex function. [References: 13]