TY - GEN
T1 - A regularized smoothing stochastic approximation (RSSA) algorithm for stochastic variational inequality problems
AU - Yousefian, Farzad
AU - Nedic, 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.
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U2 - 10.1109/WSC.2013.6721484
DO - 10.1109/WSC.2013.6721484
M3 - Conference contribution
AN - SCOPUS:84894130511
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
T2 - 2013 43rd Winter Simulation Conference - Simulation: Making Decisions in a Complex World, WSC 2013
Y2 - 8 December 2013 through 11 December 2013
ER -