Robust convex optimization
Robust convex optimization
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DOI：
10.1287/moor.23.4.769
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发表时间：
1998-11-01
影响因子：
1.7
通讯作者：
Nemirovski, A
中科院分区：
文献类型：
--
作者：
Ben-Tal, A;Nemirovski, A
我们研究的凸优化问题的数据是不明确的，它只属于一个给定的不确定性集合U，但约束必须为所有可能值的数据来自U，随后的优化问题被称为鲁棒优化。本文为鲁棒凸优化奠定了基础。在本文的主要部分，我们证明了如果U是一个椭球面不确定性集，那么对于一些最重要的一般凸优化问题（线性规划、二次约束规划、半定规划等），相应的鲁棒凸规划要么是精确的，要么是近似的，是一个可处理的问题，它适合于有效的算法，如多项式时间内点法。
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 U, yet the constraints must hold for all possible values of the data from 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 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.