Golden ratio algorithms for variational inequalities

2019/07/31 by Yura Malitsky · 232 citations
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Algorithm #Applied mathematics #Computer science #Convergence (economics) #Ergodic theory #Fixed point #Geometry #Iterated function #Lipschitz continuity #Mathematical analysis #Mathematics #Monotone polygon #Operator (biology) #Optimization and Variational Analysis #Rate of convergence #Sparse and Compressive Sensing Techniques #Strongly monotone #Variational inequality

paper · open access · doi:10.1007/s10107-019-01416-w

published in Mathematical Programming 184(1-2), 383-410 (Springer Science+Business Media)

openalex publication_date 2019/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Cited by

• Adaptive Conditional Gradient Sliding: Projection-Free and Line-Search-Free Acceleration
• On the convergence of single-call stochastic extra-gradient methods
• Explore Aggressively, Update Conservatively: Stochastic Extragradient Methods with Variable Stepsize Scaling
• Extragradient methods with complexity guarantees for hierarchical variational inequalities
• Forward-Backward-Forward Dynamical System for Solving Mixed Variational Inequality Problems
• Single-loop variance reduction methods in Bregman setups for finite-sum structured variational inequalities
• Wasserstein Distributionally Robust Nash Equilibrium Seeking with Heterogeneous Data: A Lagrangian Approach
• Adaptive extra-gradient methods for min-max optimization and games
• A golden ratio self-adaptive algorithm for solving a quasimonotone variational inequality in banach spaces
• Halpern-Type Accelerated and Splitting Algorithms For Monotone Inclusions
• New Classes of Non-monotone Variational Inequality Problems Solvable via Proximal Gradient on Smooth Gap Functions
• A novel predefined-time neurodynamic approach for mixed variational inequality problems and applications
• A Frank-Wolfe Algorithm for Strongly Monotone Variational Inequalities
• A primal-dual splitting algorithm with convex combination and larger step sizes for composite monotone inclusion problems
• Simple linesearch-free first-order methods for nonconvex optimization
• Three Operator Splitting with a Nonconvex Loss Function
• Asymptotic Properties of a Forward-Backward-Forward Differential Equation and Its Discrete Version for Solving Quasimonotone Variational Inequalities
• The Complexity of Nonconvex-Strongly-Concave Minimax Optimization
• Linesearch-free adaptive Bregman proximal gradient for convex minimization under local relative smoothness
• A Forward-Backward Splitting Method for Monotone Inclusions Without Cocoercivity
• First-order primal-dual algorithm with correction
• Accelerated Algorithms for Smooth Convex-Concave Minimax Problems with O(1/k²) Rate on Squared Gradient Norm
• Efficient Methods for Structured Nonconvex-Nonconcave Min-Max\n Optimization
• Nesterov Finds GRAAL: Optimal and Adaptive Gradient Method for Convex Optimization
• Efficient Methods for Min-Max Optimization with Dual-Linear Coupling
• Semi-Anchored Multi-Step Gradient Descent Ascent Method for Structured Nonconvex-Nonconcave Composite Minimax Problems
• Linear Last-iterate Convergence in Constrained Saddle-point Optimization
• Layer-wise Quantization for Quantized Optimistic Dual Averaging
• Two Adaptive Accelerated Golden Ratio Primal--Dual Algorithms With an Application to Poisson Imaging Problem
• Weak convergence of projection algorithm with momentum terms and new step size rule for quasimonotone variational inequalities
• New Primal-Dual Algorithm for Convex Problems
• Forward-reflected-backward method with variance reduction. [europepmc]
• Liver injury monitoring using dynamic fluorescence molecular tomography based on a time-energy difference strategy. [europepmc]
• Stochastic Primal-Dual Hybrid Gradient Algorithm with Adaptive Step Sizes. [europepmc]