Weak Convergence of a Relaxed and Inertial Hybrid Projection-Proximal Point Algorithm for Maximal Monotone Operators in Hilbert Space

Authors:
Felipe Alvarez
Affiliations:
-
Venue:
SIAM Journal on Optimization
Year:
2003

Citing 0
Cited 4

Convergence of a Hybrid Projection-Proximal Point Algorithm Coupled with Approximation Methods in Convex Optimization

Mathematics of Operations Research
Convergence theorems for inertial KM-type algorithms

Journal of Computational and Applied Mathematics
Asymptotic convergence of an inertial proximal method for unconstrained quasiconvex minimization

Journal of Global Optimization
A note on Solodov and Tseng's methods for maximal monotone mappings

Journal of Computational and Applied Mathematics

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Abstract

This paper introduces a general implicit iterative method for finding zeros of a maximal monotone operator in a Hilbert space which unifies three previously studied strategies: relaxation, inertial type extrapolation and projection step. The first two strategies are intended to speed up the convergence of the standard proximal point algorithm, while the third permits one to perform inexact proximal iterations with fixed relative error tolerance. The paper establishes the global convergence of the method for the weak topology under appropriate assumptions on the algorithm parameters.