Two fast variance-reduced proximal gradient algorithms for SMVIPs-Stochastic Mixed Variational Inequality Problems with suitable applications to stochastic network games and traffic assignment problems
In this paper, we propose two proximal gradient algorithms with variance reduction for stochastic mixed variational inequality problems. One is a proximal extragradient algorithm and another is a proximal forward–backward–forward algorithm. Under the monotonicity assumption on the mapping F and othe...
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| Vydáno v: | Journal of computational and applied mathematics Ročník 408; s. 114132 |
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Elsevier B.V
01.07.2022
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| ISSN: | 0377-0427, 1879-1778 |
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| Abstract | In this paper, we propose two proximal gradient algorithms with variance reduction for stochastic mixed variational inequality problems. One is a proximal extragradient algorithm and another is a proximal forward–backward–forward algorithm. Under the monotonicity assumption on the mapping F and other moderate conditions, we derive some asymptotic convergence properties and O(1/k) convergence rate in terms of the restricted gap function values for the proposed algorithms. Furthermore, under the bounded metric subregularity condition, we investigate the linear convergence rate and oracle complexity bounds for the proposed algorithms when the sample-size increases at a geometric rate. If the sample-size increases at a polynomial rate of ⌈k+1⌉−s with s>0, the mean-squared distance of the iterates to the solution set decays at a corresponding polynomial rate, while the iterations and oracle complexities to obtain an ε-solution are O(1/ε1/s) and O(1/ε1+1/s) respectively. Finally, some numerical experiments on stochastic network games and traffic assignment problems indicate that the proposed algorithms are efficient.
•We study a class of stochastic mixed variational inequality problems.•We present two variance-based proximal algorithms for the considered problem.•We establish asymptotic convergence and oracle complexity of the proposed algorithms.•We carry out numerical experiments on network games and traffic assignment problems. |
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| AbstractList | In this paper, we propose two proximal gradient algorithms with variance reduction for stochastic mixed variational inequality problems. One is a proximal extragradient algorithm and another is a proximal forward–backward–forward algorithm. Under the monotonicity assumption on the mapping F and other moderate conditions, we derive some asymptotic convergence properties and O(1/k) convergence rate in terms of the restricted gap function values for the proposed algorithms. Furthermore, under the bounded metric subregularity condition, we investigate the linear convergence rate and oracle complexity bounds for the proposed algorithms when the sample-size increases at a geometric rate. If the sample-size increases at a polynomial rate of ⌈k+1⌉−s with s>0, the mean-squared distance of the iterates to the solution set decays at a corresponding polynomial rate, while the iterations and oracle complexities to obtain an ε-solution are O(1/ε1/s) and O(1/ε1+1/s) respectively. Finally, some numerical experiments on stochastic network games and traffic assignment problems indicate that the proposed algorithms are efficient.
•We study a class of stochastic mixed variational inequality problems.•We present two variance-based proximal algorithms for the considered problem.•We establish asymptotic convergence and oracle complexity of the proposed algorithms.•We carry out numerical experiments on network games and traffic assignment problems. |
| ArticleNumber | 114132 |
| Author | Lin, Gui-Hua Yang, Zhen-Ping |
| Author_xml | – sequence: 1 givenname: Zhen-Ping surname: Yang fullname: Yang, Zhen-Ping email: yangzhenping1026@163.com organization: School of Mathematics, Jiaying University, Meizhou 514015, Guangdong, China – sequence: 2 givenname: Gui-Hua surname: Lin fullname: Lin, Gui-Hua email: guihualin@shu.edu.cn organization: School of Management, Shanghai University, Shanghai 200444, China |
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| Cites_doi | 10.1109/TAC.2015.2478124 10.1007/BF01580873 10.1214/aoms/1177729586 10.1007/s10589-021-00305-3 10.1214/07-AOAS131 10.1007/s10589-019-00120-x 10.1007/s11228-018-0472-9 10.1016/j.ejor.2008.09.008 10.1287/stsy.2019.0064 10.1016/j.cam.2018.12.013 10.1137/140971233 10.1137/140980910 10.1137/15M1031953 10.1007/s10107-017-1175-y 10.1007/s10107-014-0769-x 10.1137/070704277 10.1287/10-SSY011 10.1007/s10957-010-9732-z 10.1007/s10107-006-0034-z 10.1007/s11424-011-0948-2 10.1109/TAC.2008.925853 10.1142/S0217595910002569 10.1145/1961189.1961199 10.1007/s10915-021-01603-y 10.1137/17M1144799 10.1007/s11590-009-0123-z 10.1137/110825248 10.1525/9780520423671-018 10.1007/s11228-021-00591-3 10.1142/S0217595920500116 10.1080/10556788.2017.1300899 10.1109/TAC.2012.2215413 10.1007/s10107-019-01416-w 10.1016/j.cam.2010.04.036 10.1007/s101070050024 10.1007/s10957-019-01578-9 10.1007/s10957-015-0834-5 10.1109/LSP.2013.2278339 10.1007/s11228-021-00572-6 10.1007/s10957-016-1046-3 |
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| Keywords | Stochastic mixed variational inequality 90C33 Proximal algorithm Variance reduction Stochastic approximation 90C15 Nonlinear programming Complexity |
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| References | D.L. Burkholder, B.J. Davis, R.F. Gundy, Integral inequalities for convex functions of operators on martingales, in: Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 2, 1972, pp. 223-240. Malitsky (b8) 2020; 184 Yin, Madanat, Lu (b55) 2009; 198 Friedman, Hastie, Höfling, Tibshirani (b48) 2007; 1 Facchinei, Pang (b5) 2003 Shapiro, Dentcheva, Ruszczynski (b13) 2009 Yousefian, Nedić, Shanbhag (b24) 2016; 61 Noor (b10) 2009; 3 Chen, Wets, Zhang (b54) 2012; 22 Bnouhachema, Li, Khalfaoui, Sheng (b3) 2010; 234 Cui, Shanbhag (b34) 2021; 29 (b49) 2008 Chang, Lin (b51) 2011; 2 Gürkan, Özge, Robonson (b16) 1999; 84 Yang, Zhang, Wang, Lin (b37) 2021; 89 He, Gu (b6) 2009; 214 Nemirovski, A. Juditsky, Lan, Shapiro (b12) 2009; 19 Yang, Wang, Lin (b36) 2020; 37 Lin, Fukushima (b19) 2010; 6 Bertsekas (b47) 2015 Chen, Ma, Yang (b4) 2015; 25 Yang, Zhang, Zhu, Lin (b20) 2019; 352 Yousefian, Nedić, Shanbhag (b25) 2017; 165 Bot, Mertikopoulos, Staudigl, Vuong (b33) 2021; 11 Koshal, Nedić, Shanbhag (b23) 2013; 58 K. Mishchenko, D. Kovalev, E. Shulgin, Y. Malitsky, P. Richtárik, Revisiting stochastic extragradient, in: Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), Vol. 108, 2020, pp. 4573-4582. Robbins, Monro (b21) 1951; 22 Dua, Graff (b50) 2019 Ye, Yuan, Zeng, Zhang (b43) 2021; 29 Lei, Shanbhag (b14) 2020 Kannan, Shanbhag (b29) 2019; 74 Combettes, Pesquet (b42) 2015; 25 Iusem, Jofré, Oliveira, Thompsn (b32) 2017; 27 Malitsky (b9) 2018; 33 Yousefian, Nedić, Shanbhag (b30) 2018; 26 Balooee (b2) 2017; 172 Bauschke, Combettes (b39) 2011 Wang, Bertsekas (b27) 2015; 150 Condat (b52) 2013; 20 Wang, Lin, Gao, Ali (b17) 2011; 24 Li, Zhou, Huang (b7) 2016; 168 Iusem, Jofré, Thompsn (b26) 2018; 44 Juditsky, Nemirovski, Tauvel (b28) 2011; 1 Chen, Lin, Yang (b15) 2019; 20 Nesterov (b44) 2007; 109 Robbins, Siegund (b40) 1971 Xu (b18) 2010; 27 Jiang, Xu (b22) 2008; 53 Zhong, Huang (b11) 2010; 147 Duvaut, Lions (b1) 1976 Best, Chakravarti (b53) 1990; 47 Alacaoglu, Malitsky, Cevher (b45) 2021; 80 Zhang, Du, Yang, Lin (b38) 2019; 183 Iusem, Jofré, Oliveira, Thompsn (b35) 2019; 29 Böhm, Sedlmayer, Csetnek, Bot (b46) 2020 Chen (10.1016/j.cam.2022.114132_b4) 2015; 25 Yang (10.1016/j.cam.2022.114132_b20) 2019; 352 Yang (10.1016/j.cam.2022.114132_b36) 2020; 37 Zhang (10.1016/j.cam.2022.114132_b38) 2019; 183 Kannan (10.1016/j.cam.2022.114132_b29) 2019; 74 Shapiro (10.1016/j.cam.2022.114132_b13) 2009 Chang (10.1016/j.cam.2022.114132_b51) 2011; 2 Yang (10.1016/j.cam.2022.114132_b37) 2021; 89 (10.1016/j.cam.2022.114132_b49) 2008 Iusem (10.1016/j.cam.2022.114132_b35) 2019; 29 Lei (10.1016/j.cam.2022.114132_b14) 2020 Bnouhachema (10.1016/j.cam.2022.114132_b3) 2010; 234 Ye (10.1016/j.cam.2022.114132_b43) 2021; 29 Dua (10.1016/j.cam.2022.114132_b50) 2019 Yousefian (10.1016/j.cam.2022.114132_b24) 2016; 61 10.1016/j.cam.2022.114132_b31 Zhong (10.1016/j.cam.2022.114132_b11) 2010; 147 Xu (10.1016/j.cam.2022.114132_b18) 2010; 27 Nesterov (10.1016/j.cam.2022.114132_b44) 2007; 109 Yin (10.1016/j.cam.2022.114132_b55) 2009; 198 He (10.1016/j.cam.2022.114132_b6) 2009; 214 Balooee (10.1016/j.cam.2022.114132_b2) 2017; 172 Chen (10.1016/j.cam.2022.114132_b15) 2019; 20 Combettes (10.1016/j.cam.2022.114132_b42) 2015; 25 Yousefian (10.1016/j.cam.2022.114132_b30) 2018; 26 Wang (10.1016/j.cam.2022.114132_b27) 2015; 150 Jiang (10.1016/j.cam.2022.114132_b22) 2008; 53 Robbins (10.1016/j.cam.2022.114132_b40) 1971 Böhm (10.1016/j.cam.2022.114132_b46) 2020 Iusem (10.1016/j.cam.2022.114132_b26) 2018; 44 10.1016/j.cam.2022.114132_b41 Alacaoglu (10.1016/j.cam.2022.114132_b45) 2021; 80 Bertsekas (10.1016/j.cam.2022.114132_b47) 2015 Duvaut (10.1016/j.cam.2022.114132_b1) 1976 Facchinei (10.1016/j.cam.2022.114132_b5) 2003 Malitsky (10.1016/j.cam.2022.114132_b8) 2020; 184 Noor (10.1016/j.cam.2022.114132_b10) 2009; 3 Nemirovski (10.1016/j.cam.2022.114132_b12) 2009; 19 Malitsky (10.1016/j.cam.2022.114132_b9) 2018; 33 Friedman (10.1016/j.cam.2022.114132_b48) 2007; 1 Wang (10.1016/j.cam.2022.114132_b17) 2011; 24 Robbins (10.1016/j.cam.2022.114132_b21) 1951; 22 Iusem (10.1016/j.cam.2022.114132_b32) 2017; 27 Lin (10.1016/j.cam.2022.114132_b19) 2010; 6 Bauschke (10.1016/j.cam.2022.114132_b39) 2011 Yousefian (10.1016/j.cam.2022.114132_b25) 2017; 165 Gürkan (10.1016/j.cam.2022.114132_b16) 1999; 84 Best (10.1016/j.cam.2022.114132_b53) 1990; 47 Juditsky (10.1016/j.cam.2022.114132_b28) 2011; 1 Koshal (10.1016/j.cam.2022.114132_b23) 2013; 58 Condat (10.1016/j.cam.2022.114132_b52) 2013; 20 Cui (10.1016/j.cam.2022.114132_b34) 2021; 29 Chen (10.1016/j.cam.2022.114132_b54) 2012; 22 Li (10.1016/j.cam.2022.114132_b7) 2016; 168 Bot (10.1016/j.cam.2022.114132_b33) 2021; 11 |
| References_xml | – volume: 214 start-page: 26 year: 2009 end-page: 30 ident: b6 article-title: Generalized system for relaxed cocoercive mixed variational inequalities in Hilbert spaces publication-title: Appl. Math. Comput. – volume: 147 start-page: 454 year: 2010 end-page: 472 ident: b11 article-title: Stability analysis for minty mixed variational inequality in reexive Banach spaces publication-title: J. Optim. Theory Appl. – volume: 19 start-page: 1574 year: 2009 end-page: 1609 ident: b12 article-title: Robust stochastic approximation approach to stochastic programming publication-title: SIAM J. Optim. – volume: 24 start-page: 1143 year: 2011 end-page: 1153 ident: b17 article-title: Sample average approximation method for a class of stochastic variational inequality problems publication-title: J. Syst. Sci. Complex. – volume: 29 start-page: 453 year: 2021 end-page: 499 ident: b34 article-title: On the analysis of variance-reduced and randomized projection variants of single projection schemes for monotone stochastic variational inequality problems publication-title: Set-Valued Var. Anal. – volume: 183 start-page: 1053 year: 2019 end-page: 1076 ident: b38 article-title: An infeasible stochastic approximation and projection algorithm for stochastic variational inequalities publication-title: J. Optim. Theory Appl. – volume: 58 start-page: 594 year: 2013 end-page: 609 ident: b23 article-title: Regularized iterative stochastic approximation methods for stochastic variational inequality problems publication-title: IEEE Trans. Automat. Control – reference: K. Mishchenko, D. Kovalev, E. Shulgin, Y. Malitsky, P. Richtárik, Revisiting stochastic extragradient, in: Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), Vol. 108, 2020, pp. 4573-4582. – volume: 44 start-page: 236 year: 2018 end-page: 263 ident: b26 article-title: Incremental constraint projection methods for monotone stochastic variational inequalities publication-title: Math. Oper. Res. – year: 2020 ident: b14 article-title: Distributed variable sample-size gradient-response and best-response schemes for stochastic Nash games over graphs – volume: 84 start-page: 313 year: 1999 end-page: 333 ident: b16 article-title: Sample-path solution of stochastic variational inequalities publication-title: Math. Program. – start-page: 233 year: 1971 end-page: 257 ident: b40 article-title: A convergence theorem for non-negative almost supermartingales and some applications publication-title: Optimizing Methods in Statistics – volume: 198 start-page: 470 year: 2009 end-page: 479 ident: b55 article-title: Robust improvement schemes for road networks under demand uncertainty publication-title: European J. Oper. Res. – year: 2015 ident: b47 article-title: Convex Optimization Algorithms – volume: 25 start-page: 2120 year: 2015 end-page: 2142 ident: b4 article-title: A general inertial proximal point algorithm for mixed variational inequality problem publication-title: SIAM J. Optim. – volume: 22 start-page: 649 year: 2012 end-page: 673 ident: b54 article-title: Stochastic variational inequalities: residual minimization smoothing sampling average approximations publication-title: SIAM J. Optim. – volume: 6 start-page: 455 year: 2010 end-page: 482 ident: b19 article-title: Stochastic equilibrium problems and stochastic mathematical programs with equilibrium constraints: A survey publication-title: Pac. J. Optim. – volume: 61 start-page: 1753 year: 2016 end-page: 1766 ident: b24 article-title: Self-tuned stochastic approximation schemes for non-Lipschitzian stochastic multi-user optimization and Nash games publication-title: IEEE Trans. Automat. Control – volume: 11 start-page: 112 year: 2021 end-page: 139 ident: b33 article-title: Minibatch forward–backward-forward methods for solving stochastic variational inequalities publication-title: Stoch. Syst. – volume: 47 start-page: 425 year: 1990 end-page: 439 ident: b53 article-title: Active set algorithms for isotonic regression: a unifying framework publication-title: Math. Program. – year: 2019 ident: b50 article-title: UCI Machine Learning Repository – volume: 20 start-page: 149 year: 2019 end-page: 164 ident: b15 article-title: Sample average approximation method based on regularized gap function for stochastic mixed variational inequality problems publication-title: J. Nonlinear Convex Anal. – volume: 184 start-page: 383 year: 2020 end-page: 410 ident: b8 article-title: Golden ratio algorithms for variational inequalities publication-title: Math. Program. – volume: 20 start-page: 1054 year: 2013 end-page: 1057 ident: b52 article-title: A direct algorithm for 1D total variation denoising publication-title: IEEE Signal Process. Lett. – volume: 37 start-page: 1 year: 2020 end-page: 33 ident: b36 article-title: Variance-based modified backward-forward algorithm with line search for stochastic variational inequality problems and its applications publication-title: Asia-Pac. J. Oper. Res. – year: 1976 ident: b1 article-title: Inequalities in Mechanics and Physics – volume: 26 start-page: 789 year: 2018 end-page: 819 ident: b30 article-title: On stochastic mirror-prox algorithms for stochastic cartesian variational inequalities randomized block coordinate and optimal averaging schemes publication-title: Set-Valued Var. Anal. – volume: 29 start-page: 175 year: 2019 end-page: 206 ident: b35 article-title: Variance-based extragradient methods with line search for stochastic variational inequalities publication-title: SIAM J. Optim. – volume: 2 start-page: 1 year: 2011 end-page: 27 ident: b51 article-title: LIBSVM: A library for support vector machines publication-title: ACM Trans. Intell. Syst. Technol. – volume: 89 start-page: 1 year: 2021 end-page: 28 ident: b37 article-title: Variance-based subgradient extragradient method for stochastic variational inequality problems publication-title: J. Sci. Comput. – volume: 33 start-page: 140 year: 2018 end-page: 164 ident: b9 article-title: Proximal extrapolated gradient methods for variational inequalities publication-title: Optim. Methods Softw. – volume: 234 start-page: 3356 year: 2010 end-page: 3365 ident: b3 article-title: A modified inexact implicit method for mixed variational inequalities publication-title: J. Comput. Appl. Math. – volume: 25 start-page: 1221 year: 2015 end-page: 1248 ident: b42 article-title: Stochastic quasi-fejér block-coordinate fixed point iterations with random sweeping publication-title: SIAM J. Optim. – volume: 80 start-page: 321 year: 2021 end-page: 346 ident: b45 article-title: Forward-reflected-backward method with variance reduction publication-title: Comput. Optim. Appl. – year: 2008 ident: b49 article-title: Causality workbench team – volume: 150 start-page: 321 year: 2015 end-page: 363 ident: b27 article-title: Incremental constraint projection methods for variational inequalities publication-title: Math. Program. – volume: 53 start-page: 1462 year: 2008 end-page: 1475 ident: b22 article-title: Stochastic approximation approaches to the stochastic variational inequality problem publication-title: IEEE Trans. Automat. Control – volume: 29 start-page: 803 year: 2021 end-page: 837 ident: b43 article-title: Variational analysis perspective on linear convergence of some first order methods for nonsmooth convex optimization problems publication-title: Set-Valued Var. Anal. – volume: 165 start-page: 391 year: 2017 end-page: 431 ident: b25 article-title: On smoothing, regularization, and averaging in stochastic approximation methods for stochastic variational inequality problems publication-title: Math. Program. – volume: 168 start-page: 830 year: 2016 end-page: 849 ident: b7 article-title: Gap functions and global error bounds for generalized mixed variational inequalities on Hadamard manifolds publication-title: J. Optim. Theory Appl. – volume: 1 start-page: 17 year: 2011 end-page: 58 ident: b28 article-title: Solving variational inequalities with stochastic mirror-prox algorithm publication-title: Stoch. Syst. – year: 2003 ident: b5 article-title: Finite-Dimensional Variational Inequalities and Complementarity Problems – volume: 172 start-page: 774 year: 2017 end-page: 801 ident: b2 article-title: Regularized nonconvex mixed variational inequalities: Auxiliary principle technique and iterative methods publication-title: J. Optim. Theory Appl. – volume: 27 start-page: 686 year: 2017 end-page: 724 ident: b32 article-title: Extragradient method with variance reduction for stochastic variational inequalities publication-title: SIAM J. Optim. – volume: 352 start-page: 382 year: 2019 end-page: 400 ident: b20 article-title: Infeasible interior-point algorithms based on sampling average approximations for a class of stochastic complementarity problems and their applications publication-title: J. Comput. Appl. Math. – year: 2009 ident: b13 article-title: Lectures on Stochastic Programming: Modeling and Theory – volume: 1 start-page: 302 year: 2007 end-page: 332 ident: b48 article-title: Pathwise coordinate optimization publication-title: Ann. Appl. Stat. – volume: 27 start-page: 103 year: 2010 end-page: 119 ident: b18 article-title: Sample average approximation methods for a class of stochastic variational inequality problems publication-title: Asia-Pac. J. Oper. Res. – year: 2011 ident: b39 article-title: Convex Analysis and Monotone Operator Theory in Hilbert Spaces – year: 2020 ident: b46 article-title: Two steps at a time-taking GAN training in stride with Tseng’s method – volume: 74 start-page: 779 year: 2019 end-page: 820 ident: b29 article-title: Optimal stochastic extragradient schemes for pseudomonotone stochastic variational inequality problems and their variants publication-title: Comput. Optim. Appl. – volume: 22 start-page: 400 year: 1951 end-page: 407 ident: b21 article-title: A stochastic approximation method publication-title: Ann. Math. Stat. – reference: D.L. Burkholder, B.J. Davis, R.F. Gundy, Integral inequalities for convex functions of operators on martingales, in: Proceedings of the 6th Berkeley Symposium on Mathematical Statistics and Probability, Vol. 2, 1972, pp. 223-240. – volume: 109 start-page: 319 year: 2007 end-page: 344 ident: b44 article-title: Dual extrapolation and its applications to solving variational inequalities and related problems publication-title: Math. Program. – volume: 3 start-page: 437 year: 2009 end-page: 451 ident: b10 article-title: On a system of general mixed variational inequalities publication-title: Optim. Lett. – volume: 61 start-page: 1753 issue: 7 year: 2016 ident: 10.1016/j.cam.2022.114132_b24 article-title: Self-tuned stochastic approximation schemes for non-Lipschitzian stochastic multi-user optimization and Nash games publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2015.2478124 – volume: 47 start-page: 425 issue: 1 year: 1990 ident: 10.1016/j.cam.2022.114132_b53 article-title: Active set algorithms for isotonic regression: a unifying framework publication-title: Math. Program. doi: 10.1007/BF01580873 – volume: 22 start-page: 400 issue: 3 year: 1951 ident: 10.1016/j.cam.2022.114132_b21 article-title: A stochastic approximation method publication-title: Ann. Math. Stat. doi: 10.1214/aoms/1177729586 – volume: 80 start-page: 321 issue: 2 year: 2021 ident: 10.1016/j.cam.2022.114132_b45 article-title: Forward-reflected-backward method with variance reduction publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-021-00305-3 – volume: 1 start-page: 302 issue: 2 year: 2007 ident: 10.1016/j.cam.2022.114132_b48 article-title: Pathwise coordinate optimization publication-title: Ann. Appl. Stat. doi: 10.1214/07-AOAS131 – volume: 74 start-page: 779 issue: 3 year: 2019 ident: 10.1016/j.cam.2022.114132_b29 article-title: Optimal stochastic extragradient schemes for pseudomonotone stochastic variational inequality problems and their variants publication-title: Comput. Optim. Appl. doi: 10.1007/s10589-019-00120-x – year: 1976 ident: 10.1016/j.cam.2022.114132_b1 – volume: 26 start-page: 789 issue: 4 year: 2018 ident: 10.1016/j.cam.2022.114132_b30 article-title: On stochastic mirror-prox algorithms for stochastic cartesian variational inequalities randomized block coordinate and optimal averaging schemes publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-018-0472-9 – volume: 198 start-page: 470 issue: 2 year: 2009 ident: 10.1016/j.cam.2022.114132_b55 article-title: Robust improvement schemes for road networks under demand uncertainty publication-title: European J. Oper. Res. doi: 10.1016/j.ejor.2008.09.008 – volume: 11 start-page: 112 issue: 2 year: 2021 ident: 10.1016/j.cam.2022.114132_b33 article-title: Minibatch forward–backward-forward methods for solving stochastic variational inequalities publication-title: Stoch. Syst. doi: 10.1287/stsy.2019.0064 – volume: 352 start-page: 382 year: 2019 ident: 10.1016/j.cam.2022.114132_b20 article-title: Infeasible interior-point algorithms based on sampling average approximations for a class of stochastic complementarity problems and their applications publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2018.12.013 – volume: 214 start-page: 26 issue: 1 year: 2009 ident: 10.1016/j.cam.2022.114132_b6 article-title: Generalized system for relaxed cocoercive mixed variational inequalities in Hilbert spaces publication-title: Appl. Math. Comput. – year: 2009 ident: 10.1016/j.cam.2022.114132_b13 – volume: 25 start-page: 1221 issue: 2 year: 2015 ident: 10.1016/j.cam.2022.114132_b42 article-title: Stochastic quasi-fejér block-coordinate fixed point iterations with random sweeping publication-title: SIAM J. Optim. doi: 10.1137/140971233 – volume: 25 start-page: 2120 issue: 4 year: 2015 ident: 10.1016/j.cam.2022.114132_b4 article-title: A general inertial proximal point algorithm for mixed variational inequality problem publication-title: SIAM J. Optim. doi: 10.1137/140980910 – volume: 27 start-page: 686 issue: 2 year: 2017 ident: 10.1016/j.cam.2022.114132_b32 article-title: Extragradient method with variance reduction for stochastic variational inequalities publication-title: SIAM J. Optim. doi: 10.1137/15M1031953 – volume: 165 start-page: 391 issue: 1 year: 2017 ident: 10.1016/j.cam.2022.114132_b25 article-title: On smoothing, regularization, and averaging in stochastic approximation methods for stochastic variational inequality problems publication-title: Math. Program. doi: 10.1007/s10107-017-1175-y – volume: 150 start-page: 321 issue: 2 year: 2015 ident: 10.1016/j.cam.2022.114132_b27 article-title: Incremental constraint projection methods for variational inequalities publication-title: Math. Program. doi: 10.1007/s10107-014-0769-x – volume: 19 start-page: 1574 issue: 4 year: 2009 ident: 10.1016/j.cam.2022.114132_b12 article-title: Robust stochastic approximation approach to stochastic programming publication-title: SIAM J. Optim. doi: 10.1137/070704277 – volume: 1 start-page: 17 issue: 1 year: 2011 ident: 10.1016/j.cam.2022.114132_b28 article-title: Solving variational inequalities with stochastic mirror-prox algorithm publication-title: Stoch. Syst. doi: 10.1287/10-SSY011 – volume: 147 start-page: 454 issue: 3 year: 2010 ident: 10.1016/j.cam.2022.114132_b11 article-title: Stability analysis for minty mixed variational inequality in reexive Banach spaces publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-010-9732-z – volume: 109 start-page: 319 issue: 2 year: 2007 ident: 10.1016/j.cam.2022.114132_b44 article-title: Dual extrapolation and its applications to solving variational inequalities and related problems publication-title: Math. Program. doi: 10.1007/s10107-006-0034-z – volume: 24 start-page: 1143 issue: 6 year: 2011 ident: 10.1016/j.cam.2022.114132_b17 article-title: Sample average approximation method for a class of stochastic variational inequality problems publication-title: J. Syst. Sci. Complex. doi: 10.1007/s11424-011-0948-2 – volume: 53 start-page: 1462 issue: 6 year: 2008 ident: 10.1016/j.cam.2022.114132_b22 article-title: Stochastic approximation approaches to the stochastic variational inequality problem publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2008.925853 – year: 2003 ident: 10.1016/j.cam.2022.114132_b5 – volume: 27 start-page: 103 issue: 1 year: 2010 ident: 10.1016/j.cam.2022.114132_b18 article-title: Sample average approximation methods for a class of stochastic variational inequality problems publication-title: Asia-Pac. J. Oper. Res. doi: 10.1142/S0217595910002569 – year: 2011 ident: 10.1016/j.cam.2022.114132_b39 – volume: 2 start-page: 1 issue: 27 year: 2011 ident: 10.1016/j.cam.2022.114132_b51 article-title: LIBSVM: A library for support vector machines publication-title: ACM Trans. Intell. Syst. Technol. doi: 10.1145/1961189.1961199 – volume: 89 start-page: 1 issue: 1 year: 2021 ident: 10.1016/j.cam.2022.114132_b37 article-title: Variance-based subgradient extragradient method for stochastic variational inequality problems publication-title: J. Sci. Comput. doi: 10.1007/s10915-021-01603-y – volume: 29 start-page: 175 issue: 1 year: 2019 ident: 10.1016/j.cam.2022.114132_b35 article-title: Variance-based extragradient methods with line search for stochastic variational inequalities publication-title: SIAM J. Optim. doi: 10.1137/17M1144799 – volume: 44 start-page: 236 issue: 1 year: 2018 ident: 10.1016/j.cam.2022.114132_b26 article-title: Incremental constraint projection methods for monotone stochastic variational inequalities publication-title: Math. Oper. Res. – start-page: 233 year: 1971 ident: 10.1016/j.cam.2022.114132_b40 article-title: A convergence theorem for non-negative almost supermartingales and some applications – ident: 10.1016/j.cam.2022.114132_b31 – volume: 3 start-page: 437 issue: 3 year: 2009 ident: 10.1016/j.cam.2022.114132_b10 article-title: On a system of general mixed variational inequalities publication-title: Optim. Lett. doi: 10.1007/s11590-009-0123-z – volume: 22 start-page: 649 issue: 2 year: 2012 ident: 10.1016/j.cam.2022.114132_b54 article-title: Stochastic variational inequalities: residual minimization smoothing sampling average approximations publication-title: SIAM J. Optim. doi: 10.1137/110825248 – volume: 20 start-page: 149 issue: 1 year: 2019 ident: 10.1016/j.cam.2022.114132_b15 article-title: Sample average approximation method based on regularized gap function for stochastic mixed variational inequality problems publication-title: J. Nonlinear Convex Anal. – ident: 10.1016/j.cam.2022.114132_b41 doi: 10.1525/9780520423671-018 – volume: 29 start-page: 803 issue: 4 year: 2021 ident: 10.1016/j.cam.2022.114132_b43 article-title: Variational analysis perspective on linear convergence of some first order methods for nonsmooth convex optimization problems publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-021-00591-3 – year: 2020 ident: 10.1016/j.cam.2022.114132_b14 – volume: 6 start-page: 455 issue: 3 year: 2010 ident: 10.1016/j.cam.2022.114132_b19 article-title: Stochastic equilibrium problems and stochastic mathematical programs with equilibrium constraints: A survey publication-title: Pac. J. Optim. – volume: 37 start-page: 1 issue: 3 year: 2020 ident: 10.1016/j.cam.2022.114132_b36 article-title: Variance-based modified backward-forward algorithm with line search for stochastic variational inequality problems and its applications publication-title: Asia-Pac. J. Oper. Res. doi: 10.1142/S0217595920500116 – year: 2015 ident: 10.1016/j.cam.2022.114132_b47 – volume: 33 start-page: 140 issue: 1 year: 2018 ident: 10.1016/j.cam.2022.114132_b9 article-title: Proximal extrapolated gradient methods for variational inequalities publication-title: Optim. Methods Softw. doi: 10.1080/10556788.2017.1300899 – volume: 58 start-page: 594 issue: 3 year: 2013 ident: 10.1016/j.cam.2022.114132_b23 article-title: Regularized iterative stochastic approximation methods for stochastic variational inequality problems publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2012.2215413 – year: 2019 ident: 10.1016/j.cam.2022.114132_b50 – volume: 184 start-page: 383 issue: 1–2 year: 2020 ident: 10.1016/j.cam.2022.114132_b8 article-title: Golden ratio algorithms for variational inequalities publication-title: Math. Program. doi: 10.1007/s10107-019-01416-w – volume: 234 start-page: 3356 issue: 12 year: 2010 ident: 10.1016/j.cam.2022.114132_b3 article-title: A modified inexact implicit method for mixed variational inequalities publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2010.04.036 – volume: 84 start-page: 313 issue: 2 year: 1999 ident: 10.1016/j.cam.2022.114132_b16 article-title: Sample-path solution of stochastic variational inequalities publication-title: Math. Program. doi: 10.1007/s101070050024 – volume: 183 start-page: 1053 issue: 3 year: 2019 ident: 10.1016/j.cam.2022.114132_b38 article-title: An infeasible stochastic approximation and projection algorithm for stochastic variational inequalities publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-019-01578-9 – year: 2008 ident: 10.1016/j.cam.2022.114132_b49 – volume: 168 start-page: 830 issue: 3 year: 2016 ident: 10.1016/j.cam.2022.114132_b7 article-title: Gap functions and global error bounds for generalized mixed variational inequalities on Hadamard manifolds publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-015-0834-5 – volume: 20 start-page: 1054 issue: 11 year: 2013 ident: 10.1016/j.cam.2022.114132_b52 article-title: A direct algorithm for 1D total variation denoising publication-title: IEEE Signal Process. Lett. doi: 10.1109/LSP.2013.2278339 – year: 2020 ident: 10.1016/j.cam.2022.114132_b46 – volume: 29 start-page: 453 issue: 2 year: 2021 ident: 10.1016/j.cam.2022.114132_b34 article-title: On the analysis of variance-reduced and randomized projection variants of single projection schemes for monotone stochastic variational inequality problems publication-title: Set-Valued Var. Anal. doi: 10.1007/s11228-021-00572-6 – volume: 172 start-page: 774 issue: 3 year: 2017 ident: 10.1016/j.cam.2022.114132_b2 article-title: Regularized nonconvex mixed variational inequalities: Auxiliary principle technique and iterative methods publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-016-1046-3 |
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| SubjectTerms | Complexity Nonlinear programming Proximal algorithm Stochastic approximation Stochastic mixed variational inequality Variance reduction |
| Title | Two fast variance-reduced proximal gradient algorithms for SMVIPs-Stochastic Mixed Variational Inequality Problems with suitable applications to stochastic network games and traffic assignment problems |
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