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Robust solutions of uncertain quadratic and conic-quadratic problems. (English) Zbl 1026.90065
Summary: 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 the 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 essentially independent of the dimensions of the underlying conic-quadratic problem.

MSC:
90C20Quadratic programming
90C08Special problems of linear programming