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

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

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

Approximation of sparse controls in semilinear equations by piecewise linear functions

(2012) Eduardo Casas et al.   NUMERISCHE MATHEMATIK

The Łojasiewicz gradient inequality in the infinite-dimensional Hilbert space framework

(2011) Alain Haraux et al.   JOURNAL OF FUNCTIONAL ANALYSIS

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

A Continuous Dynamical Newton-Like Approach to Solving Monotone Inclusions

(2011) H. Attouch et al.   SIAM JOURNAL ON CONTROL AND OPTIMIZATION

Rank-Sparsity Incoherence for Matrix Decomposition

(2011) Venkat Chandrasekaran et al.   SIAM JOURNAL ON OPTIMIZATION

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

Interior proximal algorithm with variable metric for second-order cone programming: applications to structural optimization and support vector machines

(2010) Felipe Alvarez et al.   OPTIMIZATION METHODS & SOFTWARE

Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization

(2010) Benjamin Recht et al.   SIAM REVIEW

Characterizations of Łojasiewicz inequalities: Subgradient flows, talweg, convexity

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

Counting the Faces of Randomly-Projected Hypercubes and Orthants, with Applications

(2009) David L. Donoho et al.   DISCRETE & COMPUTATIONAL GEOMETRY

A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems

(2009) Amir Beck et al.   SIAM Journal on Imaging Sciences

Local Linear Convergence for Alternating and Averaged Nonconvex Projections

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

Constructive solution of a bilinear optimal control problem for a Schrödinger equation

(2008) Lucie Baudouin et al.   SYSTEMS & CONTROL LETTERS