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Zbl 0977.90052
Ben-Tal, A.; Nemirovski, A.
Robust convex optimization. (English)
[J] Math. Oper. Res. 23, No.4, 769-805 (1998). ISSN 1526-5471; ISSN 0364-765X/e

Summary: We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set ${\cal U}$ yet the constraints must hold for all possible values of the data from ${\cal U}$. The ensuing optimization problem is called robust optimization. In this paper we lay the foundation of robust convex optimization. In the main part of the paper we show that if ${\cal U}$ is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems (linear programming, quadratically constrained programming, semidefinite programming and others) the corresponding robust convex program is either exactly, or approximately, a tractable problem which lends itself to efficient algorithms such as polynomial time interior point methods.

MSC 2000:: *90C31 Sensitivity, etc.
65K05 Mathematical programming (numerical methods)
90C25 Convex programming
90C60 Abstract computational complexity for math. programming problems

Keywords: convex optimization; data uncertainty; robustness; linear programming; quadratic programming; semidefinite programming; geometric programming

Cited in: Zbl 1152.90630 Zbl 1136.90011 Zbl 1069.15019 Zbl 1067.65039 Zbl 1106.90365 Zbl 1026.62028

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