Robust linear semi-infinite programming duality under uncertainty

• 成果类型: Article
• 署名作者: Goberna, M. A.; Jeyakumar, V.; Li, G.; Lopez, M. A.
• 署名单位: Universitat d'Alacant; University of New South Wales Sydney
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-013-0668-6
• 发表日期: 2013
• 页码: 185-203
• 关键词: constraint qualifications; convex; optimization

摘要

In this paper, we propose a duality theory for semi-infinite linear programming problems under uncertainty in the constraint functions, the objective function, or both, within the framework of robust optimization. We present robust duality by establishing strong duality between the robust counterpart of an uncertain semi-infinite linear program and the optimistic counterpart of its uncertain Lagrangian dual. We show that robust duality holds whenever a robust moment cone is closed and convex. We then establish that the closed-convex robust moment cone condition in the case of constraint-wise uncertainty is in fact necessary and sufficient for robust duality. In other words, the robust moment cone is closed and convex if and only if robust duality holds for every linear objective function of the program. In the case of uncertain problems with affinely parameterized data uncertainty, we establish that robust duality is easily satisfied under a Slater type constraint qualification. Consequently, we derive robust forms of the Farkas lemma for systems of uncertain semi-infinite linear inequalities.