Probability Maximization with Random Linear Inequalities: Alternative Formulations and Stochastic Approximation Schemes

I. E. Bardakci, C. Lagoa, U. V. Shanbhag

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

1 Scopus citations


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 languageEnglish (US)
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)9781538654286
StatePublished - Aug 9 2018
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: Jun 27 2018Jun 29 2018

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Other2018 Annual American Control Conference, ACC 2018
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

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