On the convergence of the proximal point algorithm for convex minimization
SIAM Journal on Control and Optimization
Approximate iterations in Bregman-function-based proximal algorithms
Mathematical Programming: Series A and B
A Regularization Method for the Proximal Point Algorithm
Journal of Global Optimization
A Proximal-Projection Method for Finding Zeros of Set-Valued Operators
SIAM Journal on Control and Optimization
A note on a paper "A regularization method for the proximal point algorithm"
Journal of Global Optimization
Stability properties of the Tikhonov regularization for nonmonotone inclusions
Journal of Global Optimization
Journal of Global Optimization
Hi-index | 0.00 |
It is known, by Rockafellar (SIAM J Control Optim 14:877---898, 1976), that the proximal point algorithm (PPA) converges weakly to a zero of a maximal monotone operator in a Hilbert space, but it fails to converge strongly. Lehdili and Moudafi (Optimization 37:239---252, 1996) introduced the new prox-Tikhonov regularization method for PPA to generate a strongly convergent sequence and established a convergence property for it by using the technique of variational distance in the same space setting. In this paper, the prox-Tikhonov regularization method for the proximal point algorithm of finding a zero for an accretive operator in the framework of Banach space is proposed. Conditions which guarantee the strong convergence of this algorithm to a particular element of the solution set is provided. An inexact variant of this method with error sequence is also discussed.