Next Article in Journal
Boundedness and Applications of Fractional Integral Operators in Nonlocal Problems with Fractional Laplacians
Previous Article in Journal
The Unit Arcsine–Exponential Distribution and Its Statistical Properties with Inference and Application to Reliability Data
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Axioms
Volume 15
Issue 3
10.3390/axioms15030219
axioms-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

A Symmetry-Preserving Extrapolated Primal-Dual Hybrid Gradient Method for Saddle-Point Problems

by
Xiayang Zhang
1,
Wenzhuo Li
2,
Bowen Chang
2,
Wei Liu
3 and
Shiyu Zhang
4,*
1
School of Mathematics and Physics, School of Cryptography, Nanjing Institute of Technology, Nanjing 211167, China
2
School of Applied Technology, Nanjing Institute of Technology, Nanjing 211167, China
3
School of Automation, Nanjing Institute of Technology, Nanjing 211167, China
4
School of Communication and Artificial Intelligence, School of Integrated Circuits, Nanjing Institute of Technology, Nanjing 211167, China
*
Author to whom correspondence should be addressed.
Axioms 2026, 15(3), 219; https://doi.org/10.3390/axioms15030219
Submission received: 30 January 2026 / Revised: 3 March 2026 / Accepted: 4 March 2026 / Published: 16 March 2026
(This article belongs to the Section Mathematical Analysis)
Browse Figures
Versions Notes

Abstract

The primal-dual hybrid gradient (PDHG) method is widely used for convex–concave saddle-point problems, yet its extrapolated variants are typically asymmetric because only one side is extrapolated. We propose a symmetry-preserving refinement, E-PDHG, which performs dual-side extrapolation followed by an explicit correction step. Under standard step-size conditions, we establish global convergence for all η∈(−1,1) and derive a pointwise (non-ergodic) O(1/t) rate for the last iterate. The method does not improve the asymptotic complexity order of PDHG; instead, it enlarges the practically stable parameter region while retaining the same per-iteration cost. Numerical experiments on image deblurring/inpainting and additional machine learning benchmarks (logistic regression and LASSO) demonstrate improved finite-iteration stability and efficiency.
Keywords: primal-dual method; saddle-point problem; extrapolation; image processing; symmetry primal-dual method; saddle-point problem; extrapolation; image processing; symmetry

Share and Cite

MDPI and ACS Style

Zhang, X.; Li, W.; Chang, B.; Liu, W.; Zhang, S. A Symmetry-Preserving Extrapolated Primal-Dual Hybrid Gradient Method for Saddle-Point Problems. Axioms 2026, 15, 219. https://doi.org/10.3390/axioms15030219

AMA Style

Zhang X, Li W, Chang B, Liu W, Zhang S. A Symmetry-Preserving Extrapolated Primal-Dual Hybrid Gradient Method for Saddle-Point Problems. Axioms. 2026; 15(3):219. https://doi.org/10.3390/axioms15030219

Chicago/Turabian Style

Zhang, Xiayang, Wenzhuo Li, Bowen Chang, Wei Liu, and Shiyu Zhang. 2026. "A Symmetry-Preserving Extrapolated Primal-Dual Hybrid Gradient Method for Saddle-Point Problems" Axioms 15, no. 3: 219. https://doi.org/10.3390/axioms15030219

APA Style

Zhang, X., Li, W., Chang, B., Liu, W., & Zhang, S. (2026). A Symmetry-Preserving Extrapolated Primal-Dual Hybrid Gradient Method for Saddle-Point Problems. Axioms, 15(3), 219. https://doi.org/10.3390/axioms15030219

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop