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Concentration of Measure for Chance-Constrained Optimization

Lookup NU author(s): Dr Sadegh Soudjani

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Abstract

Chance-constrained optimization problems optimize a cost function in the presence of probabilistic constraints. They are convex in very special cases and, in practice, they are solved using approximation techniques. In this paper, we study approximation of chance constraints for the class of probability distributions that satisfy a concentration of measure property. We show that using concentration of measure, we can transform chance constraints to constraints on expectations, which can then be solved based on scenario optimization. Our approach depends solely on the concentration of measure property of the uncertainty and does not require the objective or constraint functions to be convex. We also give bounds on the required number of scenarios for achieving a certain confidence. We demonstrate our approach on a non-convex chanced-constrained optimization, and benchmark our technique against alternative approaches in the literature on chance-constrained LQG problem.


Publication metadata

Author(s): Soudjani S, Majumdar M

Editor(s): Alessandro Abate, Antoine Girard, Maurice Heemels

Publication type: Conference Proceedings (inc. Abstract)

Publication status: Published

Conference Name: 6th IFAC Conference on Analysis and Design of Hybrid Systems (ADHS 2018)

Year of Conference: 2018

Pages: 277-282

Online publication date: 31/08/2018

Acceptance date: 01/03/2018

Date deposited: 04/11/2019

ISSN: 2405-8963

Publisher: International Federation of Automatic Control

URL: https://doi.org/10.1016/j.ifacol.2018.08.047

DOI: 10.1016/j.ifacol.2018.08.047

Series Title: IFAC-PapersOnLine


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