On the nonexpansive operators based on arbitrary metric: A degenerate analysis

2021/08/07 by Xue, Feng
#47H05 #47H09 #68Q25 #90C25 #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2108.03352

Abstract

We in this paper study the nonexpansive operators equipped with arbitrary metric and investigate the connections between firm nonexpansiveness, cocoerciveness and averagedness. The convergence of the associated fixed-point iterations is discussed with particular focus on the case of degenerate metric, since the degeneracy is often encountered when reformulating many existing first-order operator splitting algorithms as a metric resolvent. This work paves a way for analyzing the generalized proximal point algorithm with a non-trivial relaxation step and degenerate metric.

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