Linear Convergence Rates for Extrapolated Fixed Point Algorithms

2018/05/10 by Bargetz, Christian, Kolobov, Victor I., Reich, Simeon +1 · 2 citations
#46N10 #46N40 #47H09 #47J25 #65F10 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1805.03932

Abstract

We establish linear convergence rates for a certain class of extrapolated fixed point algorithms which are based on dynamic string-averaging methods in a real Hilbert space. This applies, in particular, to the extrapolated simultaneous and cyclic cutter methods. Our analysis covers the cases of both metric and subgradient projections.

Cited by

• Subgradient Splitting Methods for Nonsmooth Fractional Programming with Fixed-Point Constraints
• General Perturbation Resilient Dynamic String-Averaging for Inconsistent Problems with Superiorization

Related

• Extrapolation and Local Acceleration of an Iterative Process for Common\n Fixed Point Problems
• Alternating cyclic extrapolation methods for optimization algorithms
• String-Averaging Methods for Best Approximation to Common Fixed Point\n Sets of Operators: The Finite and Infinite Cases
• Linear and strong convergence of algorithms involving averaged nonexpansive operators
• New results related to cutters and to an extrapolated block-iterative method for finding a common fixed point of a collection of them