Open Problem—Iterative Schemes for Stochastic Optimization: Convergence Statements and Limit Theorems
Published Online:17 Sep 2019https://doi.org/10.1287/stsy.2019.0043
References
- (2009) A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1):183–202.Google Scholar
- (2019) Convergence rate analysis of a stochastic trust region method via supermartingales. INFORMS J. Optim. 1(2):91–183.Google Scholar
- (2013) Stochastic trust-region response-surface method (STRONG)—A new response-surface framework for simulation optimization. INFORMS J. Comput. 25(2):230–243.Link, Google Scholar
- (2002) Stochastic Approximation and Its Applications, vol. 64 (Kluwer Academic Publishers, Dordrecht, Netherlands).Google Scholar
- (2018) Stochastic optimization using a trust-region method and random models. Math. Programming 169(2):447–487.Google Scholar
- (2012) Probability Theory: Independence, Interchangeability, Martingales (Springer-Verlag, New York).Google Scholar
- (2019) Exploiting negative curvature in deterministic and stochastic optimization. Math. Programming 176(1–2):69–94.Google Scholar
- (2007) Finite-Dimensional Variational Inequalities and Complementarity Problems (Springer-Verlag, New York).Google Scholar
- (1945) The fundamental limit theorems in probability. Bull. Amer. Math. Soc. 51(11):800–832.Google Scholar
- (2016) Accelerated gradient methods for nonconvex nonlinear and stochastic programming. Math. Programming 156(1–2):59–99.Google Scholar
- (2016) Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization. Math. Programming 155(1–2):267–305.Google Scholar
- (2019) Variance-based extragradient methods with line search for stochastic variational inequalities. SIAM J. Optim. 29(1):175–206.Google Scholar
- (2016) eg-VSSA: An extragradient variable sample-size stochastic approximation scheme: Error analysis and complexity trade-offs. 2016 Winter Simulation Conf. (WSC) (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 690–701.Google Scholar
- (2018a) A variable sample-size stochastic quasi-Newton method for smooth and nonsmooth stochastic convex optimization. 2018 IEEE Conf. Decision Control (CDC) (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 4097–4102.Google Scholar
- (2018b) Optimal smoothed variable sample-size accelerated proximal methods for structured nonsmooth stochastic convex programs. Preprint arXiv:1803.00718, submitted March 2, https://arxiv.org/abs/1803.00718.Google Scholar
- (2019) On variance reduction for stochastic smooth convex optimization with multiplicative noise. Math. Program. 174(1–2):253–292.Google Scholar
- (2011) Solving variational inequalities with stochastic mirror-prox algorithm. Stochastic Systems 1(1):17–58.Link, Google Scholar
- (2013) Regularized iterative stochastic approximation methods for stochastic variational inequality problems. IEEE Trans. Automatic Control 58(3):594–609.Google Scholar
- (2003) Stochastic Approximation and Recursive Algorithms and Applications, vol. 35 (Springer-Verlag, New York).Google Scholar
- (1922) Eine neue herleitung des exponentialgesetzes in der wahrscheinlichkeitsrechnung. Mathematische Zeitschrift 15(1):211–225.Google Scholar
- (2015) A variance reduced stochastic Newton method. Preprint arXiv:1503.08316, submitted March 28, https://arxiv.org/abs/1503.08316.Google Scholar
- (2017) Stochastic gradient descent as approximate Bayesian inference. J. Machine Learn. Res. 18(1):4873–4907.Google Scholar
- (2003) An augmented Lagrangian interior-point method using directions of negative curvature. Math. Programming 95(3):573–616.Google Scholar
- (2014) RES: Regularized stochastic BFGS algorithm. IEEE Trans. Signal Processing 62(23):6089–6104.Google Scholar
- (1983) A method for solving the convex programming problem with convergence rate of (1/k2). Soviet Math. Doklady 27(2):372–376.Google Scholar
- (2006) Numerical Optimization. (Springer-Verlag, New York).Google Scholar
- (2018) A stochastic line search method with convergence rate analysis. Preprint, submitted July 20, https://arxiv.org/abs/1807.07994.Google Scholar
- (2015) Budget-constrained stochastic approximation. Proc. 2015 Winter Simulation Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 368–379.Google Scholar
- (2018) ASTRO-DF: A class of adaptive sampling trust-region algorithms for derivative-free stochastic optimization. SIAM J. Optim. 28(4):3145–3176.Google Scholar
- (2013) A regularized smoothing stochastic approximation (RSSA) algorithm for stochastic variational inequality problems. Winter Simulations Conf.: Simulation Making Decisions Complex World, WSC 2013 (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 933–944.Google Scholar
- (2014) Optimal robust smoothing extragradient algorithms for stochastic variational inequality problems. 53rd IEEE Conf. Decision Control (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 5831–5836.Google Scholar
- (2017) On smoothing, regularization, and averaging in stochastic approximation methods for stochastic variational inequality problems. Math. Programming 165(1):391–431.Google Scholar
- (2017) Stochastic adaptive quasi-Newton methods for minimizing expected values. Proc. 34th Internat. Conf. Machine Learn. vol. 70, 4150–4159.Google Scholar

