Strong duality in robust semi-definite linear programming under data uncertainty

被引:12
|
作者
Jeyakumar, V. [1 ]
Li, G. Y. [1 ]
机构
[1] Univ New S Wales, Dept Appl Math, Sydney, NSW 2052, Australia
基金
澳大利亚研究理事会;
关键词
robust optimization; semi-definite programming under uncertainty; strong duality; linear matrix inequality problems; 90C22; 90C25; 90C46; OPTIMIZATION;
D O I
10.1080/02331934.2012.690760
中图分类号
C93 [管理学]; O22 [运筹学];
学科分类号
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要
This article develops the deterministic approach to duality for semi-definite linear programming problems in the face of data uncertainty. We establish strong duality between the robust counterpart of an uncertain semi-definite linear programming model problem and the optimistic counterpart of its uncertain dual. We prove that strong duality between the deterministic counterparts holds under a characteristic cone condition. We also show that the characteristic cone condition is also necessary for the validity of strong duality for every linear objective function of the original model problem. In addition, we derive that a robust Slater condition alone ensures strong duality for uncertain semi-definite linear programs under spectral norm uncertainty and show, in this case, that the optimistic counterpart is also computationally tractable.
引用
收藏
页码:713 / 733
页数:21
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