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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| Veröffentlicht in: | Journal of computational and applied mathematics Jg. 476; S. 117108 |
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| Sprache: | Englisch |
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01.04.2026
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| ISSN: | 0377-0427 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 117108 |
| Author | Dong, Xiaomei Wang, Shuang Gao, Xue |
| Author_xml | – sequence: 1 givenname: Shuang surname: Wang fullname: Wang, Shuang organization: Institute of Mathematics, Hebei University of Technology, Tianjin 300401, PR China – sequence: 2 givenname: Xiaomei surname: Dong fullname: Dong, Xiaomei organization: College of Sciences, Shanghai Institute of Technology, Shanghai 201418, PR China – sequence: 3 givenname: Xue surname: Gao fullname: Gao, Xue email: xgao@hebut.edu.cn organization: Institute of Mathematics, Hebei University of Technology, Tianjin 300401, PR China |
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| Cites_doi | 10.1137/20M1387213 10.1007/s10107-018-1284-2 10.1137/S1052623499354564 10.1287/moor.1100.0449 10.1007/s10208-017-9366-8 10.1137/140961791 10.1007/s10107-015-0871-8 10.1287/moor.2016.0817 10.1137/17M1138558 10.1016/S0167-6377(02)00231-6 10.1007/s10107-012-0629-5 10.1137/080716542 10.1137/16M1055323 10.1016/0041-5553(67)90040-7 10.1007/s10107-011-0484-9 10.1007/s10107-013-0701-9 10.1023/A:1023087304476 10.1137/S0363012998338806 10.1007/s10589-019-00073-1 10.1214/aos/1176348385 10.1007/BF01580089 10.1016/0041-5553(64)90137-5 10.1007/s10107-011-0472-0 10.1007/s10898-023-01300-0 |
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| Keywords | Mirror descent 49J52 Variance reduction Nonconvex nonsmooth optimization 90C26 90C15 Inertial Proximal gradient descent |
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| SubjectTerms | Inertial Mirror descent Nonconvex nonsmooth optimization Proximal gradient descent Variance reduction |
| Title | General inertial proximal stochastic mirror descent algorithm beyond Lipschitz smoothness assumption |
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