On Safe Tractable Approximations of Chance-Constrained Linear Matrix Inequalities
成果类型：
Article
署名作者：
Ben-Tal, Aharon; Nemirovski, Arkadi
署名单位：
Technion Israel Institute of Technology; University System of Georgia; Georgia Institute of Technology
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.1080.0352
发表日期：
2009
页码：
1-25
关键词：
摘要：
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.
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