Deriving robust counterparts of nonlinear uncertain inequalities

• 成果类型: Article
• 署名作者: Ben-Tal, Aharon; den Hertog, Dick; Vial, Jean-Philippe
• 署名单位: Technion Israel Institute of Technology; Tilburg University; Tilburg University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-014-0750-8
• 发表日期: 2015
• 页码: 265-299
• 关键词: optimization problems

摘要

In this paper we provide a systematic way to construct the robust counterpart of a nonlinear uncertain inequality that is concave in the uncertain parameters. We use convex analysis (support functions, conjugate functions, Fenchel duality) and conic duality in order to convert the robust counterpart into an explicit and computationally tractable set of constraints. It turns out that to do so one has to calculate the support function of the uncertainty set and the concave conjugate of the nonlinear constraint function. Conveniently, these two computations are completely independent. This approach has several advantages. First, it provides an easy structured way to construct the robust counterpart both for linear and nonlinear inequalities. Second, it shows that for new classes of uncertainty regions and for new classes of nonlinear optimization problems tractable counterparts can be derived. We also study some cases where the inequality is nonconcave in the uncertain parameters.