Robust Solutions of Uncertain Quadratic and Conic-Quadratic Problems

We consider a conic-quadratic (and in particular a quadratically constrained) optimization problem with uncertain data, known only to reside in some uncertainty set U. The robust counterpart of such a problem leads usually to an NP-hard semidefinite problem; this is the case for example when U is given as intersection of ellipsoids, or as an n-dimensional box. For these cases we build a single, explicit semidefinite program, which approximates the NP-hard robust counterpart, and we derive an estimate on the quality of the approximation, which is independent of the dimensions of the underlying conic-quadratic problem.

• Type: Journal
• Year: 2002
• Where: SIAMJO
• Authors: Aharon Ben-Tal, Arkadi Nemirovski, Cees Roos
• Keywords: Optimization Problem, Robust Counterpart, Semidefinite Problem, SIAMJO 2002