Inverse Optimization: Closed-Form Solutions, Geometry, and Goodness of Fit

Timothy C. Y. Chan (), Taewoo Lee () and Daria Terekhov ()
Additional contact information
Timothy C. Y. Chan: Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario M5S 3G8, Canada
Taewoo Lee: Department of Industrial Engineering, University of Houston, Houston, Texas 77204
Daria Terekhov: Department of Mechanical, Industrial and Aerospace Engineering, Concordia University, Montréal, Québec H3G 1M8, Canada

Management Science, 2019, vol. 65, issue 3, 1115-1135

Abstract: In classical inverse linear optimization, one assumes that a given solution is a candidate to be optimal. Real data are imperfect and noisy, so there is no guarantee that this assumption is satisfied. Inspired by regression, this paper presents a unified framework for cost function estimation in linear optimization comprising a general inverse optimization model and a corresponding goodness-of-fit metric. Although our inverse optimization model is nonconvex, we derive a closed-form solution and present the geometric intuition. Our goodness-of-fit metric, ρ , the coefficient of complementarity , has similar properties to R 2 from regression and is quasi-convex in the input data, leading to an intuitive geometric interpretation. While ρ is computable in polynomial time, we derive a lower bound that possesses the same properties, is tight for several important model variations, and is even easier to compute. We demonstrate the application of our framework for model estimation and evaluation in production planning and cancer therapy.

Keywords: inverse optimization; goodness of fit; linear programming; model estimation (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

Downloads: (external link)
https://doi.org/10.1287/mnsc.2017.2992 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:65:y:2019:i:3:p:1115-1135

Access Statistics for this article

More articles in Management Science from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().