Convex nondifferentiable stochastic optimization: A local randomized smoothing technique

Farzad Yousefian, Angelia Nedić, Uday V. Shanbhag

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

4 Scopus citations

Abstract

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.

Original languageEnglish (US)
Title of host publicationProceedings of the 2010 American Control Conference, ACC 2010
PublisherIEEE Computer Society
Pages4875-4880
Number of pages6
ISBN (Print)9781424474264
DOIs
StatePublished - 2010

Publication series

NameProceedings of the 2010 American Control Conference, ACC 2010

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

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    Yousefian, F., Nedić, A., & Shanbhag, U. V. (2010). Convex nondifferentiable stochastic optimization: A local randomized smoothing technique. In Proceedings of the 2010 American Control Conference, ACC 2010 (pp. 4875-4880). [5530908] (Proceedings of the 2010 American Control Conference, ACC 2010). IEEE Computer Society. https://doi.org/10.1109/acc.2010.5530908