Robust Solutions To Uncertain Semidefinite Programs

Robust Solutions To Uncertain Semidefinite Programs (1998)

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by Francois Oustry , Laurent El Ghaoui , Hervé Lebret

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Datum	Value	Source
TITLE	Robust Solutions To Uncertain Semidefinite Programs	user correction - Legacy Corrections
AUTHOR NAME	Francois Oustry	user correction - Legacy Corrections
AUTHOR AFFIL	AND HERV # LEBRET	user correction - Legacy Corrections
AUTHOR NAME	Laurent El Ghaoui	user correction - Legacy Corrections
AUTHOR AFFIL	AND HERV # LEBRET	user correction - Legacy Corrections
AUTHOR NAME	Hervé Lebret	user correction - Legacy Corrections
ABSTRACT	In this paper we consider semidenite programs (SDPs) whose data depends on some unknown-but-bounded perturbation parameters. We seek "robust" solutions to such programs, that is, solutions which minimize the (worst-case) objective while satisfying the constraints for every possible values of parameters within the given bounds. Assuming the data matrices are rational functions of the perturbation parameters, we show how to formulate sufficient conditions for a robust solution to exist, as SDPs. When the perturbation is "full", our conditions are necessary and sufficient. In this case, we provide sufficient conditions which guarantee that the robust solution is unique, and continuous (Hölder-stable) with respect to the unperturbed problems' data. The approach can thus be used to regularize ill-conditioned SDPs. We illustrate our results with examples taken from linear programming, maximum norm minimization, polynomial interpolation and integer programming.	user correction - Legacy Corrections
YEAR	1998	user correction - Legacy Corrections
CITATIONS	33 found	ParsCit 1.0