General inertial proximal stochastic mirror descent algorithm beyond Lipschitz smoothness assumption

In this paper, minimizing the sum of an average of finite proper closed nonconvex functions and a proper lower semicontinuous convex function over a closed convex set, is considered. We propose the general inertial proximal stochastic mirror descent (IPSMD for short) algorithm framework, which not o...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 476; p. 117108
Main Authors: Wang, Shuang, Dong, Xiaomei, Gao, Xue
Format: Journal Article
Language:English
Published: Elsevier B.V 01.04.2026
Subjects:
Inertial
Mirror descent
Nonconvex nonsmooth optimization
Proximal gradient descent
Variance reduction
Mirror descent
49J52
Variance reduction
Nonconvex nonsmooth optimization
90C26
90C15
Inertial
Proximal gradient descent
ISSN:0377-0427
Online Access:Get full text
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Summary:In this paper, minimizing the sum of an average of finite proper closed nonconvex functions and a proper lower semicontinuous convex function over a closed convex set, is considered. We propose the general inertial proximal stochastic mirror descent (IPSMD for short) algorithm framework, which not only introduces the more general inertial technique and the variance reduced gradient estimator, but also circumvents the restrictive condition of Lipschitz smoothness by using Legendre function. In theory, we establish that the sequence generated by IPSMD algorithm globally converges to the critical point, under the condition that the objective function is semialgebraic. Besides the theoretical improvement in the convergence analysis, there are also possible computational advantages which provide an interesting option for practical problems.
ISSN:0377-0427
DOI:10.1016/j.cam.2025.117108