This paper proposes a novel predictor-corrector algorithm framework for monotone inclusion problems. Many classes of problems, such as multi-block separable convex optimization problems and saddle point problems, can be reformulated as monotone inclusions, and algorithms can be designed via the proposed framework. The framework not only encompasses the relaxed forward-backward splitting method and the relaxed Davis-Yin splitting method, but also reproduces Algorithm 3.1 and Algorithm 5.1 in Chang et al (2025) by appropriately selecting the predictor steps and correction matrices, thereby simplifying their convergence analysis.
LUO Yueying
,
LIANG Tianzhe
,
CAI Xingju
. A new predictor-corrector algorithm framework for solving monotone inclusion problems[J]. Operations Research Transactions, 2026
, 30(3)
: 170
-182
.
DOI: 10.15960/j.cnki.issn.1007-6093.2026.03.010
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