Equivalent resolvents of Douglas-Rachford splitting and other operator splitting algorithms: a unified degenerate proximal point analysis
F Xue - Optimization, 2024 - Taylor & Francis
We introduce a generalized proximal point algorithm, and perform a detailed convergence
analysis with the focus on the case of degenerate metric. The degeneracy leads to a well …
analysis with the focus on the case of degenerate metric. The degeneracy leads to a well …
On the nonexpansive operators based on arbitrary metric: a degenerate analysis
F Xue - Results in Mathematics, 2022 - Springer
We in this paper study the nonexpansive operators equipped with arbitrary metric and
investigate the connections between firm nonexpansiveness, cocoerciveness and …
investigate the connections between firm nonexpansiveness, cocoerciveness and …
A generalized forward–backward splitting operator: degenerate analysis and applications
F Xue - Computational and Applied Mathematics, 2023 - Springer
In this paper, we study the nonexpansive properties of a generalized forward–backward
splitting (G-FBS) operator, particularly under the setting of degenerate metric, from which …
splitting (G-FBS) operator, particularly under the setting of degenerate metric, from which …
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 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 …
A New Criterion For Optimization Of Total Variation Denoising
F Xue, X Ai, L Gao, J Liu - 2022 International Applied …, 2022 - ieeexplore.ieee.org
Based on Chambolle's algorithm, we develop a data-driven optimization scheme based on
minimization of Stein's unbiased risk estimate (SURE)—statistically equivalent to mean …
minimization of Stein's unbiased risk estimate (SURE)—statistically equivalent to mean …