This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Ben-Tal, A. Articles by Nemirovski, A. Search for Related Content

On Safe Tractable Approximations of Chance-Constrained Linear Matrix Inequalities

Faculty of Industrial Engineering and Management, MINERVA Optimization Center, Technion–Israel Institute of Technology, Technion City, Haifa 32000, Israel
School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
abental{at}ie.technion.ac.il
nemirovs{at}isye.gatech.edu

In the paper we consider the chance-constrained version of an affinely perturbed linear matrix inequality (LMI) constraint, assuming the primitive perturbations to be independent with light-tail distributions (e.g., bounded or Gaussian). Constraints of this type, playing a central role in chance-constrained linear/conic quadratic/semidefinite programming, are typically computationally intractable. The goal of this paper is to develop a tractable approximation to these chance constraints. Our approximation is based on measure concentration results and is given by an explicit system of LMIs. Thus, the approximation is computationally tractable; moreover, it is also safe, meaning that a feasible solution of the approximation is feasible for the chance constraint.

Key Words: chance constraints; linear matrix inequalities; convex programming; measure concentration
History: Received: November 20, 2006; revision received: August 13, 2008;