The Price of Robustness for  Conic Optimization 

Dimitris Bertsimas and Melvyn Sim

MIT

In earlier proposals, the robust counterpart of   conic optimization
problems  exhibits a lateral increase in complexity, i.e., robust LPs
become SCOPs, robust SCOPs become SDPs, and robust SDPs become NP-hard. We
propose an approach that under which (a) robust conic optimization problems
retain their original structure, i.e., robust SCOPs remain SCOPs and robust
SDPs remain SDPs, (b) we establish  probabilistic guarantees for robustness
that lead to explicit ways for selecting parameters that control robustness.