@article{dac1bd4dd6864b0f84403e0a8f408830,
title = "A dynamic smoothing technique for a class of nonsmooth optimization problems on manifolds",
abstract = "We consider the problem of minimizing the sum of a smooth nonconvex function and a nonsmooth convex function over a compact embedded submanifold. We describe an algorithm, which we refer to as ``dynamic smoothing gradient descent on manifolds{"}{"} (DSGM), that is based on applying Riemmanian gradient steps on a series of smooth approximations of the objective function that are determined by a diminishing sequence of smoothing parameters. The DSGM algorithm is simple and can be easily employed for a broad class of problems without any complex adjustments. We show that all accumulation points of the sequence generated by the method are stationary. We devise a convergence rate of O( 1 k1/3 ) in terms of an optimality measure that can be easily computed. Numerical experiments illustrate the potential of the DSGM method.",
keywords = "dynamic smoothing, first-order methods, manifold optimization, rate of convergence",
author = "Amir Beck and Israel Rosset",
note = "Publisher Copyright: {\textcopyright} 2023 Society for Industrial and Applied Mathematics Publications. All rights reserved.",
year = "2023",
doi = "10.1137/22M1489447",
language = "אנגלית",
volume = "33",
pages = "1473--1493",
journal = "SIAM Journal on Optimization",
issn = "1052-6234",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "3",
}