A survey of nonlinear robust optimization

• Published in: INFOR. Information systems and operational research Vol. 58; no. 2; pp. 342 - 373
• Main Authors: Leyffer, Sven, Menickelly, Matt, Munson, Todd, Vanaret, Charlie, Wild, Stefan M.
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 01.01.2020
• Subjects: MATHEMATICS AND COMPUTING; Nonlinear robust optimization
• ISSN: 0315-5986; 1916-0615
• DOI: 10.1080/03155986.2020.1730676

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.