Mahesh Chandra Mukkamala – Optimization Online

Beyond Alternating Updates for Matrix Factorization with Inertial Bregman Proximal Gradient Algorithms

Published: 2019/05/23

Convex and Nonsmooth Optimization bregman distance, composite optimization, convex-concave backtracking, global convergence, inertial methods, matrix completion, matrix factorization, non-euclidean distances, proximal-gradient algorithms

Matrix Factorization is a popular non-convex objective, for which alternating minimization schemes are mostly used. They usually suffer from the major drawback that the solution is biased towards one of the optimization variables. A remedy is non-alternating schemes. However, due to a lack of Lipschitz continuity of the gradient in matrix factorization problems, convergence cannot … Read more

Convex-Concave Backtracking for Inertial Bregman Proximal Gradient Algorithms in Non-Convex Optimization

Published: 2019/04/11, Updated: 2019/11/05

Mahesh Chandra Mukkamala

Peter Ochs

Thomas Pock

Shoham Sabach

Convex and Nonsmooth Optimization bregman distance, composite optimization, convex-concave backtracking, global convergence, inertial methods, kurdyka-lojasiewicz inequality, non-euclidean distances, proximal-gradient algorithms

Backtracking line-search is an old yet powerful strategy for finding better step size to be used in proximal gradient algorithms. The main principle is to locally find a simple convex upper bound of the objective function, which in turn controls the step size that is used. In case of inertial proximal gradient algorithms, the situation … Read more