A survey of nonlinear robust optimization. Issue 2 (2nd April 2020)

• Record Type: Journal Article
• Authors: Leyffer, Sven; Menickelly, Matt; Munson, Todd; Vanaret, Charlie; Wild, Stefan M.
• Is Part Of: Infor. Volume 58:Issue 2(2020)
• Page Start: 342
• Page End: 373
• Publication Date: 2020-04-02
• Subjects: Nonlinear robust optimization; 90C30 -- 62K25; Operations research -- Periodicals; Electronic data processing -- Periodicals; Systems engineering -- Periodicals; Systems engineering; Electronic data processing; Periodicals; 003.05
• DOI: 10.1080/03155986.2020.1730676
• Languages: English
• ISSNs: 0315-5986

Abstract

Abstract: Robust optimization (RO) has attracted much attention from the optimization community over the past decade. RO is dedicated to solving optimization problems subject to uncertainty: design constraints must be satisfied for all the values of the uncertain parameters within a given uncertainty set. Uncertainty sets may be modeled as deterministic sets (boxes, polyhedra, ellipsoids), in which case the RO problem may be reformulated via worst-case analysis, or as families of distributions. The challenge of RO is to reformulate or approximate robust constraints so that the uncertain optimization problem is transformed into a tractable deterministic optimization problem. Most reformulation methods assume linearity of the robust constraints or uncertainty sets of favorable shape, which represents only a fraction of real-world applications. This survey addresses nonlinear RO and includes problem formulations and applications, solution approaches, and available software with code samples.