Robust solutions to uncertain semidefinite programs. (English) Zbl 0960.93007

El Ghaoui, Laurent; Oustry, Francois; Lebret, Hervé

SIAM J. Optim. 9, No. 1, 33-52 (1998).

Dealing with semidefinite programs (i.e. minimization of a linear objective under a linear matrix inequality) where data depend on unknown and bounded perturbation parameters (not necessarily small), the authors look for conditions for robust solutions. The used approach touches ideas of stochastic programming, robustness analysis of control theory and sensitivity analysis of optimization problems. A big chapter on different interesting examples is added as well as some open questions and the hint that shortly after completion of the manuscript the authors became aware of ongoing work of A. Ben-Tal and A. Nemirovski on the same subject [e.g. SIAM J. Optim. 7, No. 4, 991-1016 (1997; Zbl 0899.90133)].

Reviewer: Alfred Göpfert (Halle)

MSC:

93B35	Sensitivity (robustness)
90C31	Sensitivity, stability, parametric optimization

Keywords:

semidefinite programming; uncertainty; robustness; regularization; sensitivity

Citations:

Zbl 0899.90133

Software:

SDPHA