Robust convex optimization: A new perspective that unifies and extends

• 成果类型: Article
• 署名作者: Bertsimas, Dimitris; den Hertog, Dick; Pauphilet, Jean; Zhen, Jianzhe
• 署名单位: Massachusetts Institute of Technology (MIT); University of Amsterdam; University of London; London Business School
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-022-01881-w
• 发表日期: 2023
• 页码: 877-918

摘要

Robust convex constraints are difficult to handle, since finding the worst-case scenario is equivalent to maximizing a convex function. In this paper, we propose a new approach to deal with such constraints that unifies most approaches known in the literature and extends them in a significant way. The extension is either obtaining better solutions than the ones proposed in the literature, or obtaining solutions for classes of problems unaddressed by previous approaches. Our solution is based on an extension of the Reformulation-Linearization-Technique, and can be applied to general convex inequalities and general convex uncertainty sets. It generates a sequence of conservative approximations which can be used to obtain both upper- and lower- bounds for the optimal objective value. We illustrate the numerical benefit of our approach on a robust control and robust geometric optimization example.