### 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: Making Decisions in a Complex World, WSC 2013 |

Pages | 933-944 |

Number of pages | 12 |

DOIs | |

State | Published - 2013 |

Externally published | Yes |

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 |

### 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

### ASJC Scopus subject areas

- 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] https://doi.org/10.1109/WSC.2013.6721484

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

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

*Proceedings of the 2013 Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013.*, 6721484, 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

}

TY - GEN

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

AU - Yousefian, Farzad

AU - Nedich, Angelia

AU - Shanbhag, Uday V.

PY - 2013

Y1 - 2013

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

AN - SCOPUS:84894130511

SN - 9781479939503

SP - 933

EP - 944

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

ER -