On construction of splitting contraction algorithms in a prediction-correction framework for separable convex optimization
Abstract
In the past decade, we had developed a series of splitting contraction algorithms for separable convex optimization problems, at the root of the alternating direction method of multipliers. Convergence of these algorithms was studied under specific model-tailored conditions, while these conditions can be conceptually abstracted as two generic conditions when these algorithms are all unified as a prediction-correction framework. In this paper, in turn, we showcase a constructive way for specifying the generic convergence-guaranteeing conditions, via which new splitting contraction algorithms can be generated automatically. It becomes possible to design more application-tailored splitting contraction algorithms by specifying the prediction-correction framework, while proving their convergence is a routine.
Cite
@article{arxiv.2204.11522,
title = {On construction of splitting contraction algorithms in a prediction-correction framework for separable convex optimization},
author = {Bingsheng He and Xiaoming Yuan},
journal= {arXiv preprint arXiv:2204.11522},
year = {2022}
}