Coupled smoothing and momentum yields optimal O(1/k) global convergence plus local linear convergence under a locally strong convexity condition for nonsmooth convex optimization.
PRISMA: PRoximal Iterative SMoothing Algorithm
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abstract
Motivated by learning problems including max-norm regularized matrix completion and clustering, robust PCA and sparse inverse covariance selection, we propose a novel optimization algorithm for minimizing a convex objective which decomposes into three parts: a smooth part, a simple non-smooth Lipschitz part, and a simple non-smooth non-Lipschitz part. We use a time variant smoothing strategy that allows us to obtain a guarantee that does not depend on knowing in advance the total number of iterations nor a bound on the domain.
fields
math.OC 1years
2025 1verdicts
UNVERDICTED 1representative citing papers
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Locally Linear Convergence for Nonsmooth Convex Optimization via Coupled Smoothing and Momentum
Coupled smoothing and momentum yields optimal O(1/k) global convergence plus local linear convergence under a locally strong convexity condition for nonsmooth convex optimization.