Abstract
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.
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The research of the author was partially supported by the Singapore-MIT alliance.
The research of the author is supported by NUS academic research grant R-314-000-066-122 and the Singapore-MIT alliance.
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Bertsimas, D., Sim, M. Tractable Approximations to Robust Conic Optimization Problems. Math. Program. 107, 5–36 (2006). https://doi.org/10.1007/s10107-005-0677-1
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DOI: https://doi.org/10.1007/s10107-005-0677-1