Abstract
We first introduce and analyze an algorithm of approximating solutions of maximal monotone operators in Hilbert spaces. Using this result, we consider the convex minimization problem of finding a minimizer of a proper lower-semicontinuous convex function and the variational problem of finding a solution of a variational inequality.
Highlights
Throughout this paper, we assume that H is a real Hilbert space and T : H → 2H is a maximal monotone operator
Many researchers have studied the convergence of the sequence defined by (1.1) in a Hilbert space; see, for instance, [3,4,5,6] and the references mentioned therein
Motivated and inspired by the above result, in this paper, we suggest and analyze an iterative algorithm which has strong convergence
Summary
Throughout this paper, we assume that H is a real Hilbert space and T : H → 2H is a maximal monotone operator. Let {xn} be a sequence defined as follows: x1 = u ∈ H and xn+1 = αnu + 1 − αn Jrn xn, n = 1, 2, . Motivated and inspired by the above result, in this paper, we suggest and analyze an iterative algorithm which has strong convergence. Using this result, we consider the convex minimization problem of finding a minimizer of a proper lower-semicontinuous convex function and the variational problem of finding a solution of a variational inequality
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