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arXiv · 2302.09500

The operator splitting schemes revisited: primal-dual gap and degeneracy reduction by a unified analysis

Feng Xue
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Abstract

We revisit the operator splitting schemes proposed in a recent work of [Some extensions of the operator splitting schemes based on Lagrangian and primal-dual: A unified proximal point analysis, Feng Xue, Optimization, 2022, doi: 10.1080/02331934.2022.2057309], and further analyze the convergence of the generalized Bregman distance and the primal-dual gap of these algorithms within a unified proximal point framework. The possibility of reduction to a simple resolvent is also discussed by exploiting the structure and possible degeneracy of the underlying metric.

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Feng Xue. 2023-02-19. The operator splitting schemes revisited: primal-dual gap and degeneracy reduction by a unified analysis. https://arxiv.org/abs/2302.09500

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