nonnegative matrix and tensor factorization

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

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