### 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 language | English (US) |
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Title of host publication | Proceedings of the 2010 American Control Conference, ACC 2010 |

Publisher | IEEE Computer Society |

Pages | 4875-4880 |

Number of pages | 6 |

ISBN (Print) | 9781424474264 |

DOIs | |

State | Published - 2010 |

### Publication series

Name | Proceedings of the 2010 American Control Conference, ACC 2010 |
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### Keywords

- Local smoothing technique
- Nondifferentiable convex minimization
- Stochastic approximation method

### ASJC Scopus subject areas

- Control and Systems Engineering

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## Cite this

*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