An inertial Tseng's type proximal algorithm for nonsmooth and nonconvex\n optimization problems

2014/06/03 by Radu Ioan Boţ, Bot, Radu Ioan, Ernö Robert Csetnek +1 · 3 citations
Computer Science · Engineering · Mathematics · #65K10 #90C26 #90C30 #Advanced Optimization Algorithms Research #FOS: Mathematics #Mathematical Inequalities and Applications #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1406.0724

openalex publication_date 2014/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the convergence of a forward-backward-forward proximal-type\nalgorithm with inertial and memory effects when minimizing the sum of a\nnonsmooth function with a smooth one in the absence of convexity. The\nconvergence is obtained provided an appropriate regularization of the objective\nsatisfies the Kurdyka- Lojasiewicz inequality, which is for instance\nfulfilled for semi-algebraic functions.\n

Citations

• Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods
• Proximal alternating linearized minimization for nonconvex and nonsmooth problems
• Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality
• An inertial forward-backward-forward primal-dual splitting algorithm for solving monotone inclusion problems
• Inertial Douglas-Rachford splitting for monotone inclusion problems

Cited by

• Relaxed and inertial nonlinear Forward-Backward algorithm
• General Proximal Quasi-Newton Methods based on model functions for nonsmooth nonconvex problems
• Inertial primal-dual algorithms for structured convex optimization

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