kurdyka-lojasiewicz inequality – Page 3

An inertial Tseng’s type proximal algorithm for nonsmooth and nonconvex optimization problems

Published: 2014/06/03

Nonsmooth Optimization bregman distance, inertial proximal algorithm, kurdyka-lojasiewicz inequality, limiting subdifferential, nonsmooth optimization, tseng's type proximal algorithm

We investigate the convergence of a forward-backward-forward proximal-type algorithm with inertial and memory effects when minimizing the sum of a nonsmooth function with a smooth one in the absence of convexity. The convergence is obtained provided an appropriate regularization of the objective satisfies the Kurdyka-\L{}ojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. ArticleDownload … Read more

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

Published: 2012/08/10, Updated: 2012/09/07

Yangyang Xu

Wotao Yin

Constrained Nonlinear Optimization, Data-Mining, Nonsmooth Optimization block coordinate descent method, block multi-convex, kurdyka-lojasiewicz inequality, matrix completion, nash equilibrium, nonnegative matrix and tensor factorization, proximal gradient method, tensor completion

This paper considers regularized block multi-convex optimization, where the feasible set and objective function are generally non-convex but convex in each block of variables. We review some of its interesting examples and propose a generalized block coordinate descent method. (Using proximal updates, we further allow non-convexity over some blocks.) Under certain conditions, we show that … Read more

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

Published: 2010/12/22

Hédy Attouch

Jérôme Bolte

Benar Fux Svaiter

Nonlinear Optimization alternating direction method, block-coordinate methods, descent methods, forward-backward splitting, iterative thresholding, kurdyka-lojasiewicz inequality, nonconvex nonsmooth optimization, o-minimal structures, proximal algorithms, relative error, semi-algebraic optimization, sufficient decrease, tame optimization

In view of the minimization of a nonsmooth nonconvex function f, we prove an abstract convergence result for descent methods satisfying a sufficient-decrease assumption, and allowing a relative error tolerance. Our result guarantees the convergence of bounded sequences, under the assumption that the function f satisfies the Kurdyka-Lojasiewicz inequality. This assumption allows to cover a … Read more