Duality in robust optimization: Primal worst equals dual best. (English) Zbl 1154.90614

Summary: We study the dual problems associated with the robust counterparts of uncertain convex programs. We show that while the primal robust problem corresponds to a decision maker operating under the worst possible data, the dual problem corresponds to a decision maker operating under the \(best\) possible data.


90C46 Optimality conditions and duality in mathematical programming
90C25 Convex programming
Full Text: DOI


[1] Ben-Tal, A.; Nemirovski, A., Robust convex optimization, Math. oper. res., 23, 4, 769-805, (1998) · Zbl 0977.90052
[2] Ben-Tal, A.; Nemirovski, A., Robust optimization—methodology and applications, Math. program. ser. B, 92, 3, 453-480, (2002), ISMP 2000, Part 2 (Atlanta, GA) · Zbl 1007.90047
[3] Björck, A., Numerical methods for least-squares problems, (1996), SIAM Philadelphia, PA · Zbl 0847.65023
[4] Chandrasekaran, S.; Golub, G.H.; Gu, M.; Sayed, A.H., Efficient algorithms for least squares type problems with bounded uncertainties, (), 171-180 · Zbl 0892.62038
[5] El Ghaoui, L.; Lebret, H., Robust solution to least-squares problems with uncertain data, SIAM J. matrix anal. appl., 18, 4, 1035-1064, (1997) · Zbl 0891.65039
[6] Rockafellar, R.T., Convex analysis, (1970), Princeton Univ. Press Princeton, NJ · Zbl 0229.90020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.