A survey of nonlinear robust optimization
Abstract
Robust optimization (RO) has attracted great 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.
- Publication Date:
- Research Org.:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1660707
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- INFOR. Information Systems and Operational Research
- Additional Journal Information:
- Journal Volume: 58; Journal Issue: 2; Journal ID: ISSN 0315-5986
- Publisher:
- Taylor & Francis
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Nonlinear robust optimization
Citation Formats
Leyffer, Sven, Menickelly, Matt, Munson, Todd, Vanaret, Charlie, and Wild, Stefan M. A survey of nonlinear robust optimization. United States: N. p., 2020.
Web. doi:10.1080/03155986.2020.1730676.
Leyffer, Sven, Menickelly, Matt, Munson, Todd, Vanaret, Charlie, & Wild, Stefan M. A survey of nonlinear robust optimization. United States. https://doi.org/10.1080/03155986.2020.1730676
Leyffer, Sven, Menickelly, Matt, Munson, Todd, Vanaret, Charlie, and Wild, Stefan M. Tue .
"A survey of nonlinear robust optimization". United States. https://doi.org/10.1080/03155986.2020.1730676. https://www.osti.gov/servlets/purl/1660707.
@article{osti_1660707,
title = {A survey of nonlinear robust optimization},
author = {Leyffer, Sven and Menickelly, Matt and Munson, Todd and Vanaret, Charlie and Wild, Stefan M.},
abstractNote = {Robust optimization (RO) has attracted great 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.},
doi = {10.1080/03155986.2020.1730676},
journal = {INFOR. Information Systems and Operational Research},
number = 2,
volume = 58,
place = {United States},
year = {Tue Mar 17 00:00:00 EDT 2020},
month = {Tue Mar 17 00:00:00 EDT 2020}
}
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