### 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 language | English (US) |
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Title of host publication | Proceedings of the 2013 Winter Simulation Conference - Simulation |

Subtitle of host publication | Making Decisions in a Complex World, WSC 2013 |

Pages | 933-944 |

Number of pages | 12 |

DOIs | |

State | Published - Dec 1 2013 |

Event | 2013 43rd Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013 - Washington, DC, United States Duration: Dec 8 2013 → Dec 11 2013 |

### Publication series

Name | Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013 |
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### Other

Other | 2013 43rd Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013 |
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Country | United States |

City | Washington, DC |

Period | 12/8/13 → 12/11/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Modeling and Simulation

### Cite this

*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

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - A regularized smoothing stochastic approximation (RSSA) algorithm for stochastic variational inequality problems

AU - Yousefian, Farzad

AU - Nedic, Angelia

AU - Shanbhag, Vinayak V.

PY - 2013/12/1

Y1 - 2013/12/1

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.

UR - http://www.scopus.com/inward/record.url?scp=84894130511&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894130511&partnerID=8YFLogxK

U2 - 10.1109/WSC.2013.6721484

DO - 10.1109/WSC.2013.6721484

M3 - Conference contribution

SN - 9781479939503

T3 - Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013

SP - 933

EP - 944

BT - Proceedings of the 2013 Winter Simulation Conference - Simulation

ER -