TY - GEN
T1 - Convex nondifferentiable stochastic optimization
T2 - A local randomized smoothing technique
AU - Yousefian, Farzad
AU - Nedić, Angelia
AU - Shanbhag, Uday V.
PY - 2010
Y1 - 2010
N2 - We consider a class of stochastic nondifferentiable optimization problems where the objective function is an expectation of a random convex function, that is not necessarily differentiable. We propose a local smoothing technique, based on random local perturbations of the objective function, that lead to differentiable approximations of the function. Under the assumption that the local randomness originates from a uniform distribution, we establish a Lipschitzian property for the gradient of the approximation. This facilitates the development of a stochastic approximation framework, which now requires sampling in the product space of the original measure and the artificially introduced distribution. We show that under suitable assumptions, the resulting diminishing steplength stochastic subgradient algorithm, with two samples per iteration, converges to an optimal solution of the problem when the subgradients are bounded.
AB - We consider a class of stochastic nondifferentiable optimization problems where the objective function is an expectation of a random convex function, that is not necessarily differentiable. We propose a local smoothing technique, based on random local perturbations of the objective function, that lead to differentiable approximations of the function. Under the assumption that the local randomness originates from a uniform distribution, we establish a Lipschitzian property for the gradient of the approximation. This facilitates the development of a stochastic approximation framework, which now requires sampling in the product space of the original measure and the artificially introduced distribution. We show that under suitable assumptions, the resulting diminishing steplength stochastic subgradient algorithm, with two samples per iteration, converges to an optimal solution of the problem when the subgradients are bounded.
KW - Local smoothing technique
KW - Nondifferentiable convex minimization
KW - Stochastic approximation method
UR - http://www.scopus.com/inward/record.url?scp=77957824010&partnerID=8YFLogxK
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U2 - 10.1109/acc.2010.5530908
DO - 10.1109/acc.2010.5530908
M3 - Conference contribution
AN - SCOPUS:77957824010
SN - 9781424474264
T3 - Proceedings of the 2010 American Control Conference, ACC 2010
SP - 4875
EP - 4880
BT - Proceedings of the 2010 American Control Conference, ACC 2010
PB - IEEE Computer Society
ER -