@inproceedings{f2cd540fbc6544df81f011b1378ec04b,

title = "Probability Maximization with Random Linear Inequalities: Alternative Formulations and Stochastic Approximation Schemes",

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.",

author = "Bardakci, {I. E.} and C. Lagoa and Shanbhag, {U. V.}",

note = "Funding Information: This research is partially funded by the NSF Grant CNS-1329422 (C. Lagoa) and CMMI-1246887 (CAREER, Shanbhag) U. V. Shanbhag is in the Department of Industrial and Manuf. Engineering, udaybag@psu.edu, while I. E. Bardakci and C. Lagoa are in the Department of Electrical Engineering, the Pennsylvania State University, University Park, PA 16802, USA bardakci@psu.edu; Lagoa@engr.psu.edu. Publisher Copyright: {\textcopyright} 2018 AACC.; 2018 Annual American Control Conference, ACC 2018 ; Conference date: 27-06-2018 Through 29-06-2018",

year = "2018",

month = aug,

day = "9",

doi = "10.23919/ACC.2018.8431483",

language = "English (US)",

isbn = "9781538654286",

series = "Proceedings of the American Control Conference",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "1396--1401",

booktitle = "2018 Annual American Control Conference, ACC 2018",

address = "United States",

}