A regularized adaptive steplength stochastic approximation scheme for monotone stochastic variational inequalities

Farzad Yousefian, Angelia Nedić, Uday V. Shanbhag

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

3 Citations (Scopus)

Abstract

We consider the solution of monotone stochastic variational inequalities and present an adaptive steplength stochastic approximation framework with possibly multivalued mappings. Traditional implementations of SA have been characterized by two challenges. First, convergence of standard SA schemes requires a strongly or strictly monotone single-valued mapping, a requirement that is rarely met. Second, while convergence requires that the steplength sequences need to satisfy Σ kγ k = ∞ and Σ kγ k 2 < ∞, little guidance is provided on a choice of sequences. In fact, standard choices such as γ k = 1/k may often perform poorly in practice. Motivated by the minimization of a suitable error bound, a recursive rule for prescribing steplengths is proposed for strongly monotone problems. By introducing a regularization sequence, extensions to merely monotone regimes are proposed. Finally, an iterative smoothing extension is suggested for accommodating multivalued mappings. Preliminary numerical results suggest that the schemes prove effective.

Original languageEnglish (US)
Title of host publicationProceedings of the 2011 Winter Simulation Conference, WSC 2011
Pages4110-4121
Number of pages12
DOIs
StatePublished - Dec 1 2011
Event2011 Winter Simulation Conference, WSC 2011 - Phoenix, AZ, United States
Duration: Dec 11 2011Dec 14 2011

Publication series

NameProceedings - Winter Simulation Conference
ISSN (Print)0891-7736

Other

Other2011 Winter Simulation Conference, WSC 2011
CountryUnited States
CityPhoenix, AZ
Period12/11/1112/14/11

Fingerprint

Stochastic Approximation
Approximation Scheme
Variational Inequalities
Monotone
Multivalued Mapping
Single valued
Error Bounds
Guidance
Smoothing
Regularization
Strictly
Numerical Results
Requirements
Standards

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Computer Science Applications

Cite this

Yousefian, F., Nedić, A., & Shanbhag, U. V. (2011). A regularized adaptive steplength stochastic approximation scheme for monotone stochastic variational inequalities. In Proceedings of the 2011 Winter Simulation Conference, WSC 2011 (pp. 4110-4121). [6148100] (Proceedings - Winter Simulation Conference). https://doi.org/10.1109/WSC.2011.6148100
Yousefian, Farzad ; Nedić, Angelia ; Shanbhag, Uday V. / A regularized adaptive steplength stochastic approximation scheme for monotone stochastic variational inequalities. Proceedings of the 2011 Winter Simulation Conference, WSC 2011. 2011. pp. 4110-4121 (Proceedings - Winter Simulation Conference).
@inproceedings{b470981569d44963aacd7a8a8418dd84,
title = "A regularized adaptive steplength stochastic approximation scheme for monotone stochastic variational inequalities",
abstract = "We consider the solution of monotone stochastic variational inequalities and present an adaptive steplength stochastic approximation framework with possibly multivalued mappings. Traditional implementations of SA have been characterized by two challenges. First, convergence of standard SA schemes requires a strongly or strictly monotone single-valued mapping, a requirement that is rarely met. Second, while convergence requires that the steplength sequences need to satisfy Σ kγ k = ∞ and Σ kγ k 2 < ∞, little guidance is provided on a choice of sequences. In fact, standard choices such as γ k = 1/k may often perform poorly in practice. Motivated by the minimization of a suitable error bound, a recursive rule for prescribing steplengths is proposed for strongly monotone problems. By introducing a regularization sequence, extensions to merely monotone regimes are proposed. Finally, an iterative smoothing extension is suggested for accommodating multivalued mappings. Preliminary numerical results suggest that the schemes prove effective.",
author = "Farzad Yousefian and Angelia Nedić and Shanbhag, {Uday V.}",
year = "2011",
month = "12",
day = "1",
doi = "10.1109/WSC.2011.6148100",
language = "English (US)",
isbn = "9781457721083",
series = "Proceedings - Winter Simulation Conference",
pages = "4110--4121",
booktitle = "Proceedings of the 2011 Winter Simulation Conference, WSC 2011",

}

Yousefian, F, Nedić, A & Shanbhag, UV 2011, A regularized adaptive steplength stochastic approximation scheme for monotone stochastic variational inequalities. in Proceedings of the 2011 Winter Simulation Conference, WSC 2011., 6148100, Proceedings - Winter Simulation Conference, pp. 4110-4121, 2011 Winter Simulation Conference, WSC 2011, Phoenix, AZ, United States, 12/11/11. https://doi.org/10.1109/WSC.2011.6148100

A regularized adaptive steplength stochastic approximation scheme for monotone stochastic variational inequalities. / Yousefian, Farzad; Nedić, Angelia; Shanbhag, Uday V.

Proceedings of the 2011 Winter Simulation Conference, WSC 2011. 2011. p. 4110-4121 6148100 (Proceedings - Winter Simulation Conference).

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

TY - GEN

T1 - A regularized adaptive steplength stochastic approximation scheme for monotone stochastic variational inequalities

AU - Yousefian, Farzad

AU - Nedić, Angelia

AU - Shanbhag, Uday V.

PY - 2011/12/1

Y1 - 2011/12/1

N2 - We consider the solution of monotone stochastic variational inequalities and present an adaptive steplength stochastic approximation framework with possibly multivalued mappings. Traditional implementations of SA have been characterized by two challenges. First, convergence of standard SA schemes requires a strongly or strictly monotone single-valued mapping, a requirement that is rarely met. Second, while convergence requires that the steplength sequences need to satisfy Σ kγ k = ∞ and Σ kγ k 2 < ∞, little guidance is provided on a choice of sequences. In fact, standard choices such as γ k = 1/k may often perform poorly in practice. Motivated by the minimization of a suitable error bound, a recursive rule for prescribing steplengths is proposed for strongly monotone problems. By introducing a regularization sequence, extensions to merely monotone regimes are proposed. Finally, an iterative smoothing extension is suggested for accommodating multivalued mappings. Preliminary numerical results suggest that the schemes prove effective.

AB - We consider the solution of monotone stochastic variational inequalities and present an adaptive steplength stochastic approximation framework with possibly multivalued mappings. Traditional implementations of SA have been characterized by two challenges. First, convergence of standard SA schemes requires a strongly or strictly monotone single-valued mapping, a requirement that is rarely met. Second, while convergence requires that the steplength sequences need to satisfy Σ kγ k = ∞ and Σ kγ k 2 < ∞, little guidance is provided on a choice of sequences. In fact, standard choices such as γ k = 1/k may often perform poorly in practice. Motivated by the minimization of a suitable error bound, a recursive rule for prescribing steplengths is proposed for strongly monotone problems. By introducing a regularization sequence, extensions to merely monotone regimes are proposed. Finally, an iterative smoothing extension is suggested for accommodating multivalued mappings. Preliminary numerical results suggest that the schemes prove effective.

UR - http://www.scopus.com/inward/record.url?scp=84858042334&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858042334&partnerID=8YFLogxK

U2 - 10.1109/WSC.2011.6148100

DO - 10.1109/WSC.2011.6148100

M3 - Conference contribution

AN - SCOPUS:84858042334

SN - 9781457721083

T3 - Proceedings - Winter Simulation Conference

SP - 4110

EP - 4121

BT - Proceedings of the 2011 Winter Simulation Conference, WSC 2011

ER -

Yousefian F, Nedić A, Shanbhag UV. A regularized adaptive steplength stochastic approximation scheme for monotone stochastic variational inequalities. In Proceedings of the 2011 Winter Simulation Conference, WSC 2011. 2011. p. 4110-4121. 6148100. (Proceedings - Winter Simulation Conference). https://doi.org/10.1109/WSC.2011.6148100