Local Convergence of the Heavy-Ball Method and iPiano for Non-convex Optimization

Calculus of the Exponent of Kurdyka–Łojasiewicz Inequality and Its Applications to Linear Convergence of First-Order Methods

(2017) Guoyin Li et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

A Globally Convergent Algorithm for Nonconvex Optimization Based on Block Coordinate Update

(2017) Yangyang Xu et al.   JOURNAL OF SCIENTIFIC COMPUTING

A block coordinate variable metric forward–backward algorithm

(2016) Emilie Chouzenoux et al.   JOURNAL OF GLOBAL OPTIMIZATION

From error bounds to the complexity of first-order descent methods for convex functions

(2016) Jérôme Bolte et al.   MATHEMATICAL PROGRAMMING

Majorization-Minimization Procedures and Convergence of SQP Methods for Semi-Algebraic and Tame Programs

(2016) Jérôme Bolte et al.   MATHEMATICS OF OPERATIONS RESEARCH

Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems

(2016) Thomas Pock et al.   SIAM Journal on Imaging Sciences

An Inertial Tseng’s Type Proximal Algorithm for Nonsmooth and Nonconvex Optimization Problems

(2015) Radu Ioan Boţ et al.   JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

Douglas–Rachford splitting for nonconvex optimization with application to nonconvex feasibility problems

(2015) Guoyin Li et al.   MATHEMATICAL PROGRAMMING

A Generalized Inexact Proximal Point Method for Nonsmooth Functions that Satisfies Kurdyka Lojasiewicz Inequality

(2015) G. C. Bento et al.   Set-Valued and Variational Analysis

On Iteratively Reweighted Algorithms for Nonsmooth Nonconvex Optimization in Computer Vision

(2015) Peter Ochs et al.   SIAM Journal on Imaging Sciences

Global Convergence of Splitting Methods for Nonconvex Composite Optimization

(2015) Guoyin Li et al.   SIAM JOURNAL ON OPTIMIZATION

Splitting Methods with Variable Metric for Kurdyka–Łojasiewicz Functions and General Convergence Rates

(2014) Pierre Frankel et al.   JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

New fractional error bounds for polynomial systems with applications to Hölderian stability in optimization and spectral theory of tensors

(2014) G. Li et al.   MATHEMATICAL PROGRAMMING

iPiano: Inertial Proximal Algorithm for Nonconvex Optimization

(2014) Peter Ochs et al.   SIAM Journal on Imaging Sciences

Differential properties of the Moreau envelope

(2013) Abderrahim Jourani et al.   JOURNAL OF FUNCTIONAL ANALYSIS

Convergence of Non-smooth Descent Methods Using the Kurdyka–Łojasiewicz Inequality

(2013) Dominikus Noll   JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

Variable Metric Forward–Backward Algorithm for Minimizing the Sum of a Differentiable Function and a Convex Function

(2013) Emilie Chouzenoux et al.   JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS

Proximal alternating linearized minimization for nonconvex and nonsmooth problems

(2013) Jérôme Bolte et al.   MATHEMATICAL PROGRAMMING

A Block Coordinate Descent Method for Regularized Multiconvex Optimization with Applications to Nonnegative Tensor Factorization and Completion

(2013) Yangyang Xu et al.   SIAM Journal on Imaging Sciences

Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward–backward splitting, and regularized Gauss–Seidel methods

(2011) Hedy Attouch et al.   MATHEMATICAL PROGRAMMING

Convergence to equilibrium for the backward Euler scheme and applications

(2010) Benoît Merlet et al.   COMMUNICATIONS ON PURE AND APPLIED ANALYSIS

Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Łojasiewicz Inequality

(2010) Hédy Attouch et al.   MATHEMATICS OF OPERATIONS RESEARCH

Characterizations of Łojasiewicz inequalities: Subgradient flows, talweg, convexity

(2010) Jérôme Bolte et al.   TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY

Local Linear Convergence for Alternating and Averaged Nonconvex Projections

(2008) A. S. Lewis et al.   FOUNDATIONS OF COMPUTATIONAL MATHEMATICS

Alternating Projections on Manifolds

(2008) Adrian S. Lewis et al.   MATHEMATICS OF OPERATIONS RESEARCH