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arXiv Machine Learning By Weifeng Yang

Controlled Block Proximal Linearized Method for Nonconvex and Nonsmooth Optimization

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The paper introduces the Controlled Block Proximal Linearized (CBPL) method for multiblock nonconvex and nonsmooth optimization, avoiding assumptions of bounded iterates or objective coercivity. CBPL adds a control potential to block updates while preserving the original objective, variables, and constraints, and under explicit control design conditions and the KL property it guarantees boundedness, finite length, whole‑sequence convergence of variables, and convergence of objective values. The method is applied to graph‑regularized nonnegative matrix factorization, CP decomposition, and independent‑core matrix tri‑factorization with β0 sparsity constraints, demonstrating reconstruction‑preserving scale degeneracies, explicit controls yielding compact sublevel sets, and whole‑sequence convergence to full critical points, with experiments confirming convergence and sustained graph action.

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