### Abstract

This paper addresses a particular instance of probability maximization problems with random linear inequalities. We consider a novel approach that relies on recent findings in the context of non-Gaussian integrals of positively homogeneous functions. This allows for showing that such a maximization problem can be recast as a convex stochastic optimization problem. While standard stochastic approximation schemes cannot be directly employed, we notice that a modified variant of such schemes is provably convergent and displays optimal rates of convergence. This allows for stating a variable sample-size stochastic approximation (SA) scheme which uses an increasing sample-size of gradients at each step. This scheme is seen to provide accurate solutions at a fraction of the time compared to standard SA schemes.

Original language | English (US) |
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Title of host publication | 2018 Annual American Control Conference, ACC 2018 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1396-1401 |

Number of pages | 6 |

ISBN (Print) | 9781538654286 |

DOIs | |

State | Published - Aug 9 2018 |

Event | 2018 Annual American Control Conference, ACC 2018 - Milwauke, United States Duration: Jun 27 2018 → Jun 29 2018 |

### Publication series

Name | Proceedings of the American Control Conference |
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Volume | 2018-June |

ISSN (Print) | 0743-1619 |

### Other

Other | 2018 Annual American Control Conference, ACC 2018 |
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Country | United States |

City | Milwauke |

Period | 6/27/18 → 6/29/18 |

### All Science Journal Classification (ASJC) codes

- Electrical and Electronic Engineering

### Cite this

*2018 Annual American Control Conference, ACC 2018*(pp. 1396-1401). [8431483] (Proceedings of the American Control Conference; Vol. 2018-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ACC.2018.8431483