Tractable approximations to robust conic optimization problems
成果类型：
Article
署名作者：
Bertsimas, D; Sim, M
署名单位：
Massachusetts Institute of Technology (MIT); Massachusetts Institute of Technology (MIT); National University of Singapore
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-005-0677-1
发表日期：
2006
页码：
5-36
关键词：
摘要：
In earlier proposals, the robust counterpart of conic optimization problems exhibits a lateral increase in complexity, i.e., robust linear programming problems (LPs) become second order cone problems (SOCPs), robust SOCPs become semidefinite programming problems (SDPs), and robust SDPs become NP-hard. We propose a relaxed robust counterpart for general conic optimization problems that (a) preserves the computational tractability of the nominal problem; specifically the robust conic optimization problem retains its original structure, i.e., robust LPs remain LPs, robust SOCPs remain SOCPs and robust SDPs remain SDPs, and (b) allows us to provide a guarantee on the probability that the robust solution is feasible when the uncertain coefficients obey independent and identically distributed normal distributions.