Computable Error Bounds for Semidefinite Programming

Authors:
Sien Deng;Hui Hu
Affiliations:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA;Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA
Venue:
Journal of Global Optimization
Year:
1999

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Abstract

We study computability and applicability of error bounds for a given semidefinite pro-gramming problem under the assumption that the recession function associated with the constraint system satisfies the Slater condition. Specifically, we give computable error bounds for the distances between feasible sets, optimal objective values, and optimal solution sets in terms of an upper bound for the condition number of a constraint system, a Lipschitz constant of the objective function, and the size of perturbation. Moreover, we are able to obtain an exact penalty function for semidefinite programming along with a lower bound for penalty parameters. We also apply the results to a class of statistical problems.