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Stochastic optimization over proximally smooth sets

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arxiv 2002.06309 v1 pith:4MQLOX2Z submitted 2020-02-15 math.OC

Damek Davis , Dmitriy Drusvyatskiy , Zhan Shi This is my paper · ORCID
classification math.OC
keywords setssmoothalgorithmsoptimizationproximallystochasticalongblocks
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We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along with a retraction operation to restore feasibility. All the proposed methods come equipped with a finite time efficiency guarantee in terms of a natural stationarity measure. We discuss consequences for nonsmooth optimization over smooth manifolds and over sets cut out by weakly-convex inequalities.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Distributed Stochastic Proximal Algorithm on Riemannian Submanifolds for Weakly-convex Functions

    math.OC 2025-10 conditional novelty 6.0 of 10

    A retraction-based distributed stochastic proximal framework reaches consensus and a nearly stationary point at rate O((1+κ_g)/√k) for weakly-convex costs on compact embedded submanifolds.

  2. Riemannian EXTRA: Communication-efficient decentralized optimization over compact submanifolds with data heterogeneity

    math.OC 2025-05 reject novelty 6.0 of 10

    REXTRA claims O(1/k) convergence for decentralized manifold optimization with single-round iterate communication and constant step size, but the key contraction lemma is false as stated.

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