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...
Saved in:
| Published in: | Journal of computational and applied mathematics Vol. 476; p. 117108 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Elsevier B.V
01.04.2026
|
| Subjects: | |
| ISSN: | 0377-0427 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
|---|---|
| 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 |
| BookMark | eNp9kL1OwzAUhT0UibbwAGx-gQQ7P3YjJlRBQarE0t1y7BviqrEjX4MoT49RmZnOWb6je78VWfjggZA7zkrOuLg_lkZPZcWqtuRccrZZkCWrpSxYU8lrskI8MsZEx5slsTvwEPWJuhzJ5TLH8OWmXDAFM2pMztDJxRgitYAGfKL69B6iS-NEezgHb-nezWhGl74pTiGk0QMi1Ygf05xc8DfkatAnhNu_XJPD89Nh-1Ls33av28d9YaqWp6Kzm17YljfNwIUGKWQHmtd9Z6Vt7GD6XloGjRAV00NdaQG1lZ2xzHLZMlGvCb_MmhgQIwxqjvmTeFacqV8z6qiyGfVrRl3MZObhwkC-69NBVGgceAPWRTBJ2eD-oX8A54dzBg |
| 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 |
| ContentType | Journal Article |
| Copyright | 2025 Elsevier B.V. |
| Copyright_xml | – notice: 2025 Elsevier B.V. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.cam.2025.117108 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| ExternalDocumentID | 10_1016_j_cam_2025_117108 S0377042725006223 |
| GroupedDBID | --K --M -~X .~1 0R~ 1B1 1RT 1~. 1~5 29K 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9DU 9JN AABNK AAEDT AAEDW AAFWJ AAIKJ AAKOC AALRI AAOAW AAQFI AAQXK AATTM AAXKI AAXUO AAYWO ABAOU ABDPE ABEFU ABFNM ABJNI ABMAC ABWVN ABXDB ACDAQ ACGFS ACLOT ACRLP ACRPL ACVFH ADBBV ADCNI ADEZE ADMUD ADNMO ADVLN AEBSH AEIPS AEKER AENEX AEUPX AEXQZ AFJKZ AFPUW AFTJW AGHFR AGQPQ AGUBO AGYEJ AHHHB AIEXJ AIGII AIGVJ AIIUN AIKHN AITUG AKBMS AKRWK AKYEP ALMA_UNASSIGNED_HOLDINGS AMRAJ ANKPU APXCP ARUGR ASPBG AVWKF AXJTR AZFZN BKOJK BLXMC CS3 D-I DU5 EBS EFJIC EFKBS EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FEDTE FGOYB FIRID FNPLU FYGXN G-2 G-Q GBLVA HVGLF HZ~ IHE IXB J1W KOM LG9 M26 M41 MHUIS MO0 N9A NHB O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 R2- RNS ROL RPZ SDF SDG SDP SES SEW SPC SPCBC SSW SSZ T5K TN5 UPT WUQ XPP YQT ZMT ZY4 ~02 ~G- ~HD AAYXX CITATION |
| ID | FETCH-LOGICAL-c251t-9d8b6d5144f16ae7679ea13b9d7d4dfcbb7d0e46620af32a6e3d79cd0d175063 |
| ISICitedReferencesCount | 0 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001590442700003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0377-0427 |
| IngestDate | Thu Nov 27 01:09:35 EST 2025 Wed Dec 10 14:32:03 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | Mirror descent 49J52 Variance reduction Nonconvex nonsmooth optimization 90C26 90C15 Inertial Proximal gradient descent |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c251t-9d8b6d5144f16ae7679ea13b9d7d4dfcbb7d0e46620af32a6e3d79cd0d175063 |
| ParticipantIDs | crossref_primary_10_1016_j_cam_2025_117108 elsevier_sciencedirect_doi_10_1016_j_cam_2025_117108 |
| PublicationCentury | 2000 |
| PublicationDate | April 2026 2026-04-00 |
| PublicationDateYYYYMMDD | 2026-04-01 |
| PublicationDate_xml | – month: 04 year: 2026 text: April 2026 |
| PublicationDecade | 2020 |
| PublicationTitle | Journal of computational and applied mathematics |
| PublicationYear | 2026 |
| Publisher | Elsevier B.V |
| Publisher_xml | – name: Elsevier B.V |
| References | Lu (b20) 2019; 1 Bertsekas (b8) 2011; 129 Censor, Iusem, Zenios (b15) 1998; 81 Bauschke, Combettes (b4) 2011 Zhang, Barrio, Martínez, Jiang, Cheng (b27) 2019; 7 Attouch, Bolte, Svaiter (b23) 2013; 137 Rish, Grabarnik (b3) 2014 Nesterov (b7) 2013; 140 Li, Pong (b30) 2018; 18 Han (b16) 2003; 26 Bregman (b21) 1967; 7 Bolte, Sabach, Teboulle (b24) 2014; 146 Driggs, Tang, Liang, Davies, Schönlieb (b10) 2021; 14 Xiao, Zhang (b2) 2014; 24 Beck, Teboulle (b17) 2003; 31 Beck, Teboulle (b6) 2009; 2 Wen, Chen, Pong (b25) 2017; 27 Bauschke, Bolte, Teboulle (b14) 2016; 42 Tseng (b5) 2000; 38 Gao, Cai, Wang, Han (b29) 2023; 87 Bolte, Sabach, Teboulle, Vaisbourd (b1) 2018; 28 Wu, Li (b26) 2019; 73 Csiszar (b31) 1991; 19 Ben-Tal, Margalit, Nemirovski (b18) 2001; 12 Teboulle (b19) 2018; 170 Nesterov (b13) 2004 Polyak (b12) 1964; 4 Rényi (b28) 2007 Defazio, Bach, Lacoste-Julien (b9) 2014; 27 Attouch, Bolte, Redont, Soubeyran (b22) 2010; 35 Ghadimi, Lan (b11) 2016; 156 Beck (10.1016/j.cam.2025.117108_b17) 2003; 31 Nesterov (10.1016/j.cam.2025.117108_b7) 2013; 140 Bertsekas (10.1016/j.cam.2025.117108_b8) 2011; 129 Bolte (10.1016/j.cam.2025.117108_b24) 2014; 146 Gao (10.1016/j.cam.2025.117108_b29) 2023; 87 Csiszar (10.1016/j.cam.2025.117108_b31) 1991; 19 Bauschke (10.1016/j.cam.2025.117108_b14) 2016; 42 Attouch (10.1016/j.cam.2025.117108_b22) 2010; 35 Beck (10.1016/j.cam.2025.117108_b6) 2009; 2 Zhang (10.1016/j.cam.2025.117108_b27) 2019; 7 Ghadimi (10.1016/j.cam.2025.117108_b11) 2016; 156 Bolte (10.1016/j.cam.2025.117108_b1) 2018; 28 Polyak (10.1016/j.cam.2025.117108_b12) 1964; 4 Rényi (10.1016/j.cam.2025.117108_b28) 2007 Rish (10.1016/j.cam.2025.117108_b3) 2014 Tseng (10.1016/j.cam.2025.117108_b5) 2000; 38 Nesterov (10.1016/j.cam.2025.117108_b13) 2004 Ben-Tal (10.1016/j.cam.2025.117108_b18) 2001; 12 Li (10.1016/j.cam.2025.117108_b30) 2018; 18 Teboulle (10.1016/j.cam.2025.117108_b19) 2018; 170 Driggs (10.1016/j.cam.2025.117108_b10) 2021; 14 Bauschke (10.1016/j.cam.2025.117108_b4) 2011 Wu (10.1016/j.cam.2025.117108_b26) 2019; 73 Defazio (10.1016/j.cam.2025.117108_b9) 2014; 27 Han (10.1016/j.cam.2025.117108_b16) 2003; 26 Attouch (10.1016/j.cam.2025.117108_b23) 2013; 137 Lu (10.1016/j.cam.2025.117108_b20) 2019; 1 Censor (10.1016/j.cam.2025.117108_b15) 1998; 81 Wen (10.1016/j.cam.2025.117108_b25) 2017; 27 Xiao (10.1016/j.cam.2025.117108_b2) 2014; 24 Bregman (10.1016/j.cam.2025.117108_b21) 1967; 7 |
| References_xml | – year: 2004 ident: b13 article-title: Introductory Lectures on Convex Optimization: A Basic Course – volume: 27 start-page: 124 year: 2017 end-page: 145 ident: b25 article-title: Linear convergence of proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth minimization problems publication-title: SIAM J. Optim. – year: 2007 ident: b28 article-title: Probability Theory – volume: 35 start-page: 438 year: 2010 end-page: 457 ident: b22 article-title: Proximal alternating minimization and projection methods for nonconvex problems: An approach based on the Kurdyka–Łojasiewicz inequality publication-title: Math. Oper. Res. – volume: 146 start-page: 459 year: 2014 end-page: 494 ident: b24 article-title: Proximal alternating linearized minimization for nonconvex and nonsmooth problems publication-title: Math. Program. – volume: 18 start-page: 1199 year: 2018 end-page: 1232 ident: b30 article-title: Calculus of the exponent of Kurdyka–Łjasiewicz inequality and its applications to linear convergence of first-order methods publication-title: Found. Comput. Math. – volume: 19 start-page: 2032 year: 1991 end-page: 2066 ident: b31 article-title: Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems publication-title: Ann. Stat. – volume: 129 start-page: 163 year: 2011 end-page: 195 ident: b8 article-title: Incremental proximal methods for large scale convex optimization publication-title: Math. Program. – volume: 38 start-page: 431 year: 2000 end-page: 446 ident: b5 article-title: A modified forward–backward splitting method for maximal monotone mappings publication-title: SIAM J. Control Optim. – volume: 7 start-page: 200 year: 1967 end-page: 217 ident: b21 article-title: The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming publication-title: USSR Comput. Math. Math. Phys. – volume: 42 start-page: 330 year: 2016 end-page: 348 ident: b14 article-title: A descent lemma beyond Lipschitz gradient continuity: First-order methods revisited and applications publication-title: Math. Oper. Res. – volume: 28 start-page: 2131 year: 2018 end-page: 2151 ident: b1 article-title: First order methods beyond convexity and Lipschitz gradient continuity with applications to quadratic inverse problems publication-title: SIAM J. Optim. – volume: 137 start-page: 91 year: 2013 end-page: 129 ident: b23 article-title: Convergence of descent methods for semi-algebraic and tame problems: Proximal algorithms, forward-backward splitting, and regularized Gauss–Seidel methods publication-title: Math. Program. – volume: 1 start-page: 288 year: 2019 end-page: 303 ident: b20 article-title: Relative-continuity for non-Lipschitz non-smooth convex optimization using stochastic (or deterministic) mirror descent publication-title: Inf. J. Optim. – volume: 81 start-page: 373 year: 1998 end-page: 400 ident: b15 article-title: An interior point method with Bregman functions for the variational inequality problem with paramonotone operators publication-title: Math. Program. – volume: 27 start-page: 1646 year: 2014 end-page: 1654 ident: b9 article-title: SAGA: A fast incremental gradient method with support for non-strongly convex composite objectives publication-title: Adv. Neural Inf. Process. Syst. – volume: 24 start-page: 2057 year: 2014 end-page: 2075 ident: b2 article-title: A proximal stochastic gradient method with progressive variance reduction publication-title: SIAM J. Optim. – year: 2014 ident: b3 article-title: Sparse Modeling: Theory, Algorithms, and Applications – volume: 7 year: 2019 ident: b27 article-title: Bregman proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth minimization problems publication-title: IEEE Access – year: 2011 ident: b4 article-title: Convex Analysis and Monotone Operator Theory in Hilbert Spaces – volume: 31 start-page: 167 year: 2003 end-page: 175 ident: b17 article-title: Mirror descent and nonlinear projected subgradient methods for convex optimization publication-title: Oper. Res. Lett. – volume: 140 start-page: 125 year: 2013 end-page: 161 ident: b7 article-title: Gradient methods for minimizing composite functions publication-title: Math. Program. – volume: 170 start-page: 67 year: 2018 end-page: 96 ident: b19 article-title: A simplified view of first order methods for optimization publication-title: Math. Program. – volume: 73 start-page: 129 year: 2019 end-page: 158 ident: b26 article-title: General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems publication-title: Comput. Optim. Appl. – volume: 4 start-page: 1 year: 1964 end-page: 17 ident: b12 article-title: Some methods of speeding up the convergence of iteration methods publication-title: USSR Comput. Math. Math. Phys. – volume: 12 start-page: 79 year: 2001 end-page: 108 ident: b18 article-title: The ordered subsets mirror descent optimization method with applications to tomography publication-title: SIAM J. Optim. – volume: 2 start-page: 183 year: 2009 end-page: 202 ident: b6 article-title: A fast iterative shrinkage-thresholding algorithm for linear inverse problems publication-title: SIAM J. Imaging Sci. – volume: 156 start-page: 59 year: 2016 end-page: 99 ident: b11 article-title: Accelerated gradient methods for nonconvex nonlinear and stochastic programming publication-title: Math. Program. – volume: 87 start-page: 277 year: 2023 end-page: 300 ident: b29 article-title: An alternating structure-adapted bregman proximal gradient descent algorithm for constrained nonconvex nonsmooth optimization problems and its inertial variant publication-title: J. Global Optim. – volume: 14 start-page: 1932 year: 2021 end-page: 1970 ident: b10 article-title: A stochastic proximal alternating minimization for nonsmooth and nonconvex optimization publication-title: SIAM J. Imaging Sci. – volume: 26 start-page: 125 year: 2003 end-page: 140 ident: b16 article-title: A new hybrid generalized proximal point algorithm for variational inequality problems publication-title: J. Global Optim. – volume: 14 start-page: 1932 issue: 4 year: 2021 ident: 10.1016/j.cam.2025.117108_b10 article-title: A stochastic proximal alternating minimization for nonsmooth and nonconvex optimization publication-title: SIAM J. Imaging Sci. doi: 10.1137/20M1387213 – volume: 170 start-page: 67 year: 2018 ident: 10.1016/j.cam.2025.117108_b19 article-title: A simplified view of first order methods for optimization publication-title: Math. Program. doi: 10.1007/s10107-018-1284-2 – year: 2014 ident: 10.1016/j.cam.2025.117108_b3 – volume: 12 start-page: 79 issue: 1 year: 2001 ident: 10.1016/j.cam.2025.117108_b18 article-title: The ordered subsets mirror descent optimization method with applications to tomography publication-title: SIAM J. Optim. doi: 10.1137/S1052623499354564 – volume: 35 start-page: 438 issue: 2 year: 2010 ident: 10.1016/j.cam.2025.117108_b22 article-title: Proximal alternating minimization and projection methods for nonconvex problems: An approach based on the Kurdyka–Łojasiewicz inequality publication-title: Math. Oper. Res. doi: 10.1287/moor.1100.0449 – volume: 18 start-page: 1199 year: 2018 ident: 10.1016/j.cam.2025.117108_b30 article-title: Calculus of the exponent of Kurdyka–Łjasiewicz inequality and its applications to linear convergence of first-order methods publication-title: Found. Comput. Math. doi: 10.1007/s10208-017-9366-8 – volume: 24 start-page: 2057 issue: 4 year: 2014 ident: 10.1016/j.cam.2025.117108_b2 article-title: A proximal stochastic gradient method with progressive variance reduction publication-title: SIAM J. Optim. doi: 10.1137/140961791 – volume: 156 start-page: 59 year: 2016 ident: 10.1016/j.cam.2025.117108_b11 article-title: Accelerated gradient methods for nonconvex nonlinear and stochastic programming publication-title: Math. Program. doi: 10.1007/s10107-015-0871-8 – volume: 42 start-page: 330 issue: 2 year: 2016 ident: 10.1016/j.cam.2025.117108_b14 article-title: A descent lemma beyond Lipschitz gradient continuity: First-order methods revisited and applications publication-title: Math. Oper. Res. doi: 10.1287/moor.2016.0817 – volume: 28 start-page: 2131 issue: 3 year: 2018 ident: 10.1016/j.cam.2025.117108_b1 article-title: First order methods beyond convexity and Lipschitz gradient continuity with applications to quadratic inverse problems publication-title: SIAM J. Optim. doi: 10.1137/17M1138558 – volume: 31 start-page: 167 issue: 3 year: 2003 ident: 10.1016/j.cam.2025.117108_b17 article-title: Mirror descent and nonlinear projected subgradient methods for convex optimization publication-title: Oper. Res. Lett. doi: 10.1016/S0167-6377(02)00231-6 – volume: 140 start-page: 125 year: 2013 ident: 10.1016/j.cam.2025.117108_b7 article-title: Gradient methods for minimizing composite functions publication-title: Math. Program. doi: 10.1007/s10107-012-0629-5 – volume: 2 start-page: 183 issue: 1 year: 2009 ident: 10.1016/j.cam.2025.117108_b6 article-title: A fast iterative shrinkage-thresholding algorithm for linear inverse problems publication-title: SIAM J. Imaging Sci. doi: 10.1137/080716542 – volume: 27 start-page: 124 issue: 1 year: 2017 ident: 10.1016/j.cam.2025.117108_b25 article-title: Linear convergence of proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth minimization problems publication-title: SIAM J. Optim. doi: 10.1137/16M1055323 – volume: 7 start-page: 200 issue: 3 year: 1967 ident: 10.1016/j.cam.2025.117108_b21 article-title: The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming publication-title: USSR Comput. Math. Math. Phys. doi: 10.1016/0041-5553(67)90040-7 – volume: 7 year: 2019 ident: 10.1016/j.cam.2025.117108_b27 article-title: Bregman proximal gradient algorithm with extrapolation for a class of nonconvex nonsmooth minimization problems publication-title: IEEE Access – volume: 137 start-page: 91 year: 2013 ident: 10.1016/j.cam.2025.117108_b23 article-title: Convergence of descent methods for semi-algebraic and tame problems: Proximal algorithms, forward-backward splitting, and regularized Gauss–Seidel methods publication-title: Math. Program. doi: 10.1007/s10107-011-0484-9 – volume: 1 start-page: 288 issue: 4 year: 2019 ident: 10.1016/j.cam.2025.117108_b20 article-title: Relative-continuity for non-Lipschitz non-smooth convex optimization using stochastic (or deterministic) mirror descent publication-title: Inf. J. Optim. – volume: 146 start-page: 459 year: 2014 ident: 10.1016/j.cam.2025.117108_b24 article-title: Proximal alternating linearized minimization for nonconvex and nonsmooth problems publication-title: Math. Program. doi: 10.1007/s10107-013-0701-9 – volume: 26 start-page: 125 year: 2003 ident: 10.1016/j.cam.2025.117108_b16 article-title: A new hybrid generalized proximal point algorithm for variational inequality problems publication-title: J. Global Optim. doi: 10.1023/A:1023087304476 – volume: 38 start-page: 431 issue: 2 year: 2000 ident: 10.1016/j.cam.2025.117108_b5 article-title: A modified forward–backward splitting method for maximal monotone mappings publication-title: SIAM J. Control Optim. doi: 10.1137/S0363012998338806 – year: 2004 ident: 10.1016/j.cam.2025.117108_b13 – volume: 73 start-page: 129 year: 2019 ident: 10.1016/j.cam.2025.117108_b26 article-title: General inertial proximal gradient method for a class of nonconvex nonsmooth optimization problems publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-019-00073-1 – volume: 19 start-page: 2032 issue: 4 year: 1991 ident: 10.1016/j.cam.2025.117108_b31 article-title: Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems publication-title: Ann. Stat. doi: 10.1214/aos/1176348385 – volume: 27 start-page: 1646 year: 2014 ident: 10.1016/j.cam.2025.117108_b9 article-title: SAGA: A fast incremental gradient method with support for non-strongly convex composite objectives publication-title: Adv. Neural Inf. Process. Syst. – volume: 81 start-page: 373 year: 1998 ident: 10.1016/j.cam.2025.117108_b15 article-title: An interior point method with Bregman functions for the variational inequality problem with paramonotone operators publication-title: Math. Program. doi: 10.1007/BF01580089 – volume: 4 start-page: 1 issue: 5 year: 1964 ident: 10.1016/j.cam.2025.117108_b12 article-title: Some methods of speeding up the convergence of iteration methods publication-title: USSR Comput. Math. Math. Phys. doi: 10.1016/0041-5553(64)90137-5 – year: 2007 ident: 10.1016/j.cam.2025.117108_b28 – volume: 129 start-page: 163 year: 2011 ident: 10.1016/j.cam.2025.117108_b8 article-title: Incremental proximal methods for large scale convex optimization publication-title: Math. Program. doi: 10.1007/s10107-011-0472-0 – volume: 87 start-page: 277 year: 2023 ident: 10.1016/j.cam.2025.117108_b29 article-title: An alternating structure-adapted bregman proximal gradient descent algorithm for constrained nonconvex nonsmooth optimization problems and its inertial variant publication-title: J. Global Optim. doi: 10.1007/s10898-023-01300-0 – year: 2011 ident: 10.1016/j.cam.2025.117108_b4 |
| SSID | ssj0006914 |
| Score | 2.4670868 |
| Snippet | 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... |
| SourceID | crossref elsevier |
| SourceType | Index Database Publisher |
| StartPage | 117108 |
| SubjectTerms | Inertial Mirror descent Nonconvex nonsmooth optimization Proximal gradient descent Variance reduction |
| Title | General inertial proximal stochastic mirror descent algorithm beyond Lipschitz smoothness assumption |
| URI | https://dx.doi.org/10.1016/j.cam.2025.117108 |
| Volume | 476 |
| WOSCitedRecordID | wos001590442700003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: ScienceDirect Freedom Collection - Elsevier issn: 0377-0427 databaseCode: AIEXJ dateStart: 20211213 customDbUrl: isFulltext: true dateEnd: 99991231 titleUrlDefault: https://www.sciencedirect.com omitProxy: false ssIdentifier: ssj0006914 providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1Lb9QwELaWlgMcUHmpD0A-cCIKytvxsUJFFEHFYSVyi_wKm6pJVtlsVfrrO07sJJRWogcu0SrKeqN8n8bfTma-Qeg9j6NApp5yhfJi3ZITugyUgxumPCUKJEEkeD9sgpydpVlGfywWv20vzOUFqev06oqu_yvUcA7A1q2zD4B7XBROwGcAHY4AOxz_CXhjJO3orr5O58N1pUpZ9X0hjVgxbczsVGXbNno2eG_m5LCLX01bdqvK4UNHy7dyvdFvGK6dTdUAmH1ABJ0N4I9I_i1pRT8iwqYXextYI3Kr0R121PA_baZ6tWVm-9SC2pQIZyVrKlWO5UGsT-lmWzVPUwTJrLrFtGcR4urBHvPQG5F58PR9kDvpnXF9SDGcw3927R4QxB-na__00L61t40Vh7aY7TyHJXK9RD4s8QjtBiSmENN3j09Psq_jNp7QwRje3rd9Jd4XB966j7tFzUyoLPfQMwMHPh6Y8RwtVP0CPf0-AfASScMRbDmCLUfwxBE8cAQbjuCRI3jgCB45gieO4Ikjr9Dy88ny0xfXjNtwBYjczqUy5YkEAR0VfsIUSQhVzA85lURGshCcE-mpKEkCjxVhwBIVSkKF9CRIUFC6r9FO3dRqH2FVME4o8QghIoqLlIe-LJgSQZQGlPviAH2wjytfD6Yq-b0AHaDIPtDcqMJB7eVAjvu_dviQ3zhCTybOvkE7XbtVb9FjcdmVm_adYcYNFy-Imw |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=General+inertial+proximal+stochastic+mirror+descent+algorithm+beyond+Lipschitz+smoothness+assumption&rft.jtitle=Journal+of+computational+and+applied+mathematics&rft.au=Wang%2C+Shuang&rft.au=Dong%2C+Xiaomei&rft.au=Gao%2C+Xue&rft.date=2026-04-01&rft.issn=0377-0427&rft.volume=476&rft.spage=117108&rft_id=info:doi/10.1016%2Fj.cam.2025.117108&rft.externalDBID=n%2Fa&rft.externalDocID=10_1016_j_cam_2025_117108 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0377-0427&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0377-0427&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0377-0427&client=summon |