New Primal-Dual Algorithms for a Class of Nonsmooth and Nonlinear Convex-Concave Minimax Problems

DOI10.1137/21M1408683zbMath1504.90195MaRDI QIDQ5043287

Yuzixuan Zhu, Quoc Tran Dinh, Deyi Liu

Publication date: 21 October 2022

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

zbMATH Keywords

primal-dual algorithmoptimal convergence rateNesterov's accelerated schemeconvex cone constrained programconvex-concave minimax problemlast-iterate convergence rate

Mathematics Subject Classification ID

Convex programming (90C25) Large-scale problems in mathematical programming (90C06) Minimax problems in mathematical programming (90C47)

Uses Software

• LIBSVM
• ElemStatLearn
• Wasserstein GAN

Cites Work

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• Smooth minimization of non-smooth functions
• A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms
• Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators
• Dual extrapolation and its applications to solving variational inequalities and related problems
• Introductory lectures on convex optimization. A basic course.
• Accelerated schemes for a class of variational inequalities
• A first-order primal-dual algorithm for convex problems with applications to imaging
• A splitting algorithm for dual monotone inclusions involving cocoercive operators
• Iteration complexity of inexact augmented Lagrangian methods for constrained convex programming
• Proximal Splitting Methods in Signal Processing
• Convergence Analysis of Primal-Dual Algorithms for a Saddle-Point Problem: From Contraction Perspective
• Convergence Rate Analysis of Primal-Dual Splitting Schemes
• On the Complexity of the Hybrid Proximal Extragradient Method for the Iterates and the Ergodic Mean
• Complexity of Variants of Tseng's Modified F-B Splitting and Korpelevich's Methods for Hemivariational Inequalities with Applications to Saddle-point and Convex Optimization Problems
• A Minimax Theorem with Applications to Machine Learning, Signal Processing, and Finance
• An Accelerated HPE-Type Algorithm for a Class of Composite Convex-Concave Saddle-Point Problems
• An accelerated non-Euclidean hybrid proximal extragradient-type algorithm for convex–concave saddle-point problems
• A Smooth Primal-Dual Optimization Framework for Nonsmooth Composite Convex Minimization
• On a Class of Minimax Stochastic Programs
• Prox-Method with Rate of Convergence O(1/t) for Variational Inequalities with Lipschitz Continuous Monotone Operators and Smooth Convex-Concave Saddle Point Problems
• Finite-Dimensional Variational Inequalities and Complementarity Problems
• Non-stationary First-Order Primal-Dual Algorithms with Faster Convergence Rates
• Rate of Convergence Analysis of Decomposition Methods Based on the Proximal Method of Multipliers for Convex Minimization
• A Primal-Dual Algorithm with Line Search for General Convex-Concave Saddle Point Problems
• Faster Lagrangian-Based Methods in Convex Optimization
• Accelerated Stochastic Algorithms for Convex-Concave Saddle-Point Problems
• Inertial, Corrected, Primal-Dual Proximal Splitting
• Convergence Rate of $\mathcal{O}(1/k)$ for Optimistic Gradient and Extragradient Methods in Smooth Convex-Concave Saddle Point Problems
• Solving variational inequalities with Stochastic Mirror-Prox algorithm
• Excessive Gap Technique in Nonsmooth Convex Minimization
• Combining Convex–Concave Decompositions and Linearization Approaches for Solving BMIs, With Application to Static Output Feedback
• Convex analysis and monotone operator theory in Hilbert spaces

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