The operator splitting schemes revisited: primal-dual gap and degeneracy reduction by a unified analysis
F Xue - Optimization Letters, 2024 - Springer
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 …
the operator splitting schemes based on Lagrangian and primal-dual: A unified proximal …
On degenerate metric resolvent
F Xue - arXiv preprint arXiv:2401.08431, 2024 - arxiv.org
We study the basic properties of resolvent equipped with degenerate metric, in particular,
the issues of full domain, single-valuedness and weak convergence in the whole space …
the issues of full domain, single-valuedness and weak convergence in the whole space …
On Douglas-Rachford splitting that generally fails to be a proximal mapping: a degenerate proximal point analysis
F Xue - Optimization, 2024 - Taylor & Francis
Based on a degenerate proximal point analysis, we show that the Douglas-Rachford
splitting can be reduced to a well-defined resolvent, but generally fails to be a proximal …
splitting can be reduced to a well-defined resolvent, but generally fails to be a proximal …
On the metric resolvent: nonexpansiveness, convergence rates and applications
F Xue - Journal of the Operations Research Society of China, 2023 - Springer
In this paper, we study the nonexpansive properties of metric resolvent and present the
convergence analysis for the associated fixed-point iterations of both Banach–Picard and …
convergence analysis for the associated fixed-point iterations of both Banach–Picard and …