Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming
Publication type: Journal Article
Publication date: 2013-12-03
scimago Q1
wos Q1
SJR: 1.388
CiteScore: 4.7
Impact factor: 2.3
ISSN: 10526234, 10957189
Software
Theoretical Computer Science
Abstract
In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this method possesses a nearly optimal rate of convergence if the problem is convex. We discuss a variant of the algorithm which consists of applying a post-optimization phase to evaluate a short list of solutions generated by several independent runs of the RSG method, and show that such modification allows to improve significantly the large-deviation properties of the algorithm. These methods are then specialized for solving a class of simulation-based optimization problems in which only stochastic zeroth-order information is available.
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581
Total citations:
581
Citations from 2024:
218
(37.52%)
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Ghadimi S., Lan G. Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming // SIAM Journal on Optimization. 2013. Vol. 23. No. 4. pp. 2341-2368.
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Ghadimi S., Lan G. Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming // SIAM Journal on Optimization. 2013. Vol. 23. No. 4. pp. 2341-2368.
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TY - JOUR
DO - 10.1137/120880811
UR - https://doi.org/10.1137/120880811
TI - Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming
T2 - SIAM Journal on Optimization
AU - Ghadimi, Saeed
AU - Lan, Guanghui
PY - 2013
DA - 2013/12/03
PB - Society for Industrial and Applied Mathematics (SIAM)
SP - 2341-2368
IS - 4
VL - 23
SN - 1052-6234
SN - 1095-7189
ER -
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@article{2013_Ghadimi,
author = {Saeed Ghadimi and Guanghui Lan},
title = {Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming},
journal = {SIAM Journal on Optimization},
year = {2013},
volume = {23},
publisher = {Society for Industrial and Applied Mathematics (SIAM)},
month = {dec},
url = {https://doi.org/10.1137/120880811},
number = {4},
pages = {2341--2368},
doi = {10.1137/120880811}
}
Cite this
MLA
Copy
Ghadimi, Saeed, and Guanghui Lan. “Stochastic First- and Zeroth-Order Methods for Nonconvex Stochastic Programming.” SIAM Journal on Optimization, vol. 23, no. 4, Dec. 2013, pp. 2341-2368. https://doi.org/10.1137/120880811.