@Article{JCM-42-3,
author = {Yuhong, Dai and Wang, Jiani and Zhang, Liwei},
title = {Semi-Proximal Point Method for Nonsmooth Convex-Concave Minimax Optimization},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {42},
number = {3},
pages = {617--637},
abstract = {<p style="text-align: justify;">Minimax optimization problems are an important class of optimization problems arising
from modern machine learning and traditional research areas. While there have been many
numerical algorithms for solving smooth convex-concave minimax problems, numerical
algorithms for nonsmooth convex-concave minimax problems are rare. This paper aims
to develop an efficient numerical algorithm for a structured nonsmooth convex-concave
minimax problem. A semi-proximal point method (SPP) is proposed, in which a quadratic
convex-concave function is adopted for approximating the smooth part of the objective
function and semi-proximal terms are added in each subproblem. This construction enables
the subproblems at each iteration are solvable and even easily solved when the semiproximal
terms are cleverly chosen. We prove the global convergence of our algorithm under mild
assumptions, without requiring strong convexity-concavity condition. Under the locally
metrical subregularity of the solution mapping, we prove that our algorithm has the linear
rate of convergence. Preliminary numerical results are reported to verify the efficiency of
our algorithm.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2301-m2022-0099},
url = {https://global-sci.com/article/91071/semi-proximal-point-method-for-nonsmooth-convex-concave-minimax-optimization}
}