References
- Gower RM, Schmidt M, Bach F, et al. Variance-reduced methods for machine learning. Proceedings of the IEEE. 2020 Oct 16;108:1968–1983.
- Nitanda A. Stochastic proximal gradient descent with acceleration techniques. In: Advances in Neural Information Processing Systems. Montreal Canada, December 8-13, 2014. p. 1574-1582.Montreal: MIT press
- Xiao L, Zhang T. A proximal stochastic gradient method with progressive variance reduction. SIAM J Optim. 2014;24:2057–2075.
- Allen-Zhu Z, Hazan E. Variance reduction for faster non-convex optimization. Proceedings of the 33rd International Conference on Machine Learning, 2016 Jun 20–22; New York, USA, Vol. 48, 2016. p. 699–707. JMLR.org.
- Balamurugan P, Bach F. Stochastic variance reduction methods for saddle-point problems. In: Advances in neural information processing systems. Barcelona Spain, December 5-10, 2016. p. 1416–1424. Barcelona: Curran Associates Inc.
- Devraj AM, Chen J. Stochastic variance reduced primal dual algorithms for empirical composition optimization. In: Advances in neural information processing systems. Vancouver Canada, December 8-14, 2019. p. 9882–9892. Vancouver: Curran Associates, Inc.
- Du SS, Hu W. Linear convergence of the primal–dual gradient method for convexconcave saddle point problems without strong convexity. In: Proceedings of the International Conference on Artificial Intelligence and Statistics, Naha, Okinawa, Japan, April 16–18, 2019. p. 196–205, PMLR.
- Hamedani EY, Jalilzadeh A. A stochastic variance-reduced accelerated primal-dual method for finite-sum saddle-point problems. https://arxiv.org/abs/2012.13456.
- Shi Z, Zhang X, Yu Y. Bregman divergence for stochastic variance reduction: saddle-point and adversarial prediction. In: Advances in neural information processing systems, Long Beach, CA, USA , Dec 4–9, 2017. p. 6033–6043. Curran Associates, Inc.
- Combettes PL, Pesquet J-C. Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators. Set-Valued Var Anal. 2012;20:307–330.
- Iyiola OS, Enyi CD, Shehu Y. Reflected three-operator splitting method for monotone inclusion problem. Optim Methods Softw. 2021. doi:10.1080/10556788.2021.1924715 .
- Boţ RI, Hendrich C. A Douglas–Rachford type primal–dual method for solving inclusions with mixtures of composite and parallel-sum type monotone operators. SIAM J Optim. 2013;23:2541–2565.
- Boţ RI, Hendrich C. Convergence analysis for a primal–dual monotone + skew splitting algorithm with applications to total variation minimization. J Math Imaging Vis. 2014;49:551–568.
- Bùi MN, Combettes PL. Multivariate monotone inclusions in saddle form. Mathematics of Operations Research. 2021.
- Ryu EK, Vũ BC. Finding the forward-Douglas–Rachford-forward method. J Optim Theory Appl. 2020;184:858–876.
- Vũ BC. A splitting algorithm for dual monotone inclusions involving cocoercive operators. Adv Comput Math. 2013;38:667–681.
- Combettes PL, Pesquet J-C. Stochastic approximations and perturbations in forward–backward splitting for monotone operators. Pure Appl Funct Anal. 2016;1(1):13–37.
- Nguyen VD, Vũ BC. Convergence analysis of the stochastic reflected forward–backward splitting algorithm. https://arxiv.org/abs/2102.08906.
- Rosasco L, Villa S, Vũ BC. A stochastic inertial forward–backward splitting algorithm for multivariate monotone inclusions. Optimization. 2016;65:1293–1314.
- Rosasco L, Villa S, Vũ BC. A first-order stochastic primal–dual algorithm with correction step. Numer Funct Anal Optim. 2017;38:602–626.
- Bregman LM. The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming. USSR Comput Math Math Phys. 1967;7:200–217.
- Bauschke HH, Borwein JM, Combettes PL. Bregman monotone optimization algorithms. SIAM J Control Optim. 2003;42:596–636.
- Bùi MN, Combettes PL. Bregman forward–backward operator splitting. Set-Valued Var Anal. 2021;29:583–603.
- Chen G, Teboulle M. Convergence analysis of aproximal-like minimization algorithm using Bregman functions. SIAM J Optim. 1993;3:538–543.
- Dang CD, Lan G. Stochastic block mirror descent methods for nonsmooth and stochastic optimization. SIAM J Optim. 2015;25:856–881.
- Duchi JC, Shalev-Shwartz S, Singer Y, et al. Composite objective mirror descent. In: COLT, Haifa, Israel, Jun 27–29, 2010. p. 14–26, Omnipress.
- Lu H, Freund R, Nesterov Y. Relatively smooth convex optimization by first-order methods, and applications. SIAM J Optim. 2018;28:333–354.
- Hien LTK, Lu C, Xu H, et al. Accelerated stochastic mirror descent algorithms for composite non-strongly convex optimization. J Optim Theory Appl. 2019;181:541–566.
- Lei Y, Zhou DX. Analysis of online composite mirror descent algorithm. Neural Comput. 2017;29:825–860.
- Nemirovski A, Juditsky A, Lan G, et al. Robust stochastic approximation approach to stochastic programming. SIAM J Optim. 2009;19(4):1574–1609.
- Van Nguyen Q. Forward-backward splitting with Bregman distances. Vietnam J Math. 2017;45:519–539.
- Tseng P. On accelerated proximal gradient methods for convex–concave optimization. Technical report, Department of Mathematics, University of Washington. 2008.
- Chen Y, Lan G, Ouyang Y. Optimal primal–dual methods for a class of saddle point problems. SIAM J Optim. 2014;24:1779–1814.
- Bauschke HH, Borwein JM, Combettes PL. Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces. Commun Contemp Math. 2001;3:615–647.
- Moreau JJ. Fonctionnelles sous-différentiables. C R Acad Sci Paris Sér A Math. 1963;257:4117–4119.
- Cevher V, Vũ BC. A reflected forward-backward splitting method for monotone inclusions involving Lipschitzian operators. Set-Valued Var Anal. 2021;29:163–174.
- Boţ RI, Csetnek ER, Meier D. Inducing strong convergence into the asymptotic behaviour of proximal splitting algorithms in Hilbert spaces. Optim Methods Softw. 2019;34:489–514.
- Juditsky A, Nemirovski AS, Tauvel C. Solving variational inequalities with stochastic mirror-prox algorithm. Stochastic Syst. 2011;1:17–58.
- Zhao R. Optimal stochastic algorithms for convex–concave saddle-point problems. Mathematics of Operations Research. 2021.
- Wang J, Xiao L. Exploiting strong convexity from data with primal-dual first-order algorithms. In: International Conference on Machine Learning, 2017 Aug 6–11; Sydney, Australia, Vol. 70, 2017. p. 3694–3702. JMLR. org.
- Boţ RI, Csetnek ER, Hendrich C. On the convergence rate improvement of a primal–dual splitting algorithm for solving monotone inclusion problems. Math Program. 2015;150:251–279.
- Chambolle A, Pock T. On the ergodic convergence rates of a first-order primal–dual algorithm. Math Program. 2016;159:253–287.
- Drori Y, Sabach S, Teboulle M. A simple algorithm for a class of nonsmooth convex–concave saddle-point problems. Oper Res Lett. 2015;43:209–214.
- Hamedani EY, Aybat NS. A primal–dual algorithm with line search for general convex–concave saddle point problems. SIAM J Optim. 2021;31:1299–1329.