A regularized smoothing stochastic approximation (RSSA) algorithm for stochastic variational inequality problems

Farzad Yousefian, Angelia Nedic, Vinayak V. Shanbhag

Research output: Chapter in Book/Report/Conference proceedingConference contribution

10 Citations (Scopus)

Abstract

We consider a stochastic variational inequality (SVI) problem with a continuous and monotone mapping over a compact and convex set. Traditionally, stochastic approximation (SA) schemes for SVIs have relied on strong monotonicity and Lipschitzian properties of the underlying map. We present a regularized smoothedSA(RSSA) schemewherein the stepsize, smoothing, and regularization parametersare diminishing sequences. Under suitable assumptions on the sequences, we show that the algorithm generates iterates that converge to a solution in an almost-sure sense. Additionally, we provide rate estimates that relate iterates to their counterparts derived from the Tikhonov trajectory associated with a deterministic problem.

Original languageEnglish (US)
Title of host publicationProceedings of the 2013 Winter Simulation Conference - Simulation
Subtitle of host publicationMaking Decisions in a Complex World, WSC 2013
Pages933-944
Number of pages12
DOIs
StatePublished - Dec 1 2013
Event2013 43rd Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013 - Washington, DC, United States
Duration: Dec 8 2013Dec 11 2013

Publication series

NameProceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013

Other

Other2013 43rd Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013
CountryUnited States
CityWashington, DC
Period12/8/1312/11/13

Fingerprint

Stochastic Approximation
Stochastic Algorithms
Variational Inequality Problem
Approximation algorithms
Iterate
Smoothing
Approximation Algorithms
Trajectories
Monotone Mapping
Diminishing
Approximation Scheme
Compact Set
Convex Sets
Monotonicity
Regularization
Trajectory
Converge
Estimate

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation

Cite this

Yousefian, F., Nedic, A., & Shanbhag, V. V. (2013). A regularized smoothing stochastic approximation (RSSA) algorithm for stochastic variational inequality problems. In Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013 (pp. 933-944). [6721484] (Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013). https://doi.org/10.1109/WSC.2013.6721484
Yousefian, Farzad ; Nedic, Angelia ; Shanbhag, Vinayak V. / A regularized smoothing stochastic approximation (RSSA) algorithm for stochastic variational inequality problems. Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013. 2013. pp. 933-944 (Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013).
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abstract = "We consider a stochastic variational inequality (SVI) problem with a continuous and monotone mapping over a compact and convex set. Traditionally, stochastic approximation (SA) schemes for SVIs have relied on strong monotonicity and Lipschitzian properties of the underlying map. We present a regularized smoothedSA(RSSA) schemewherein the stepsize, smoothing, and regularization parametersare diminishing sequences. Under suitable assumptions on the sequences, we show that the algorithm generates iterates that converge to a solution in an almost-sure sense. Additionally, we provide rate estimates that relate iterates to their counterparts derived from the Tikhonov trajectory associated with a deterministic problem.",
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Yousefian, F, Nedic, A & Shanbhag, VV 2013, A regularized smoothing stochastic approximation (RSSA) algorithm for stochastic variational inequality problems. in Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013., 6721484, Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013, pp. 933-944, 2013 43rd Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013, Washington, DC, United States, 12/8/13. https://doi.org/10.1109/WSC.2013.6721484

A regularized smoothing stochastic approximation (RSSA) algorithm for stochastic variational inequality problems. / Yousefian, Farzad; Nedic, Angelia; Shanbhag, Vinayak V.

Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013. 2013. p. 933-944 6721484 (Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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N2 - We consider a stochastic variational inequality (SVI) problem with a continuous and monotone mapping over a compact and convex set. Traditionally, stochastic approximation (SA) schemes for SVIs have relied on strong monotonicity and Lipschitzian properties of the underlying map. We present a regularized smoothedSA(RSSA) schemewherein the stepsize, smoothing, and regularization parametersare diminishing sequences. Under suitable assumptions on the sequences, we show that the algorithm generates iterates that converge to a solution in an almost-sure sense. Additionally, we provide rate estimates that relate iterates to their counterparts derived from the Tikhonov trajectory associated with a deterministic problem.

AB - We consider a stochastic variational inequality (SVI) problem with a continuous and monotone mapping over a compact and convex set. Traditionally, stochastic approximation (SA) schemes for SVIs have relied on strong monotonicity and Lipschitzian properties of the underlying map. We present a regularized smoothedSA(RSSA) schemewherein the stepsize, smoothing, and regularization parametersare diminishing sequences. Under suitable assumptions on the sequences, we show that the algorithm generates iterates that converge to a solution in an almost-sure sense. Additionally, we provide rate estimates that relate iterates to their counterparts derived from the Tikhonov trajectory associated with a deterministic problem.

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Yousefian F, Nedic A, Shanbhag VV. A regularized smoothing stochastic approximation (RSSA) algorithm for stochastic variational inequality problems. In Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013. 2013. p. 933-944. 6721484. (Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013). https://doi.org/10.1109/WSC.2013.6721484