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Zbl 1134.90026
Bertsimas, Dimitris; Sim, Melvyn
Tractable approximations to robust conic optimization problems. (English)
[J] Math. Program. 107, No. 1-2 (B), 5-36 (2006). ISSN 0025-5610; ISSN 1436-4646/e

Summary: 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.

MSC 2000:: *90C15 Stochastic programming
90C31 Sensitivity, etc.

Keywords: robust optimization; conic optimization; stochastic optimization

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