15th EUROPT Workshop on Advances in Continuous Optimization

Montréal, Canada, 12 — 14 juillet 2017

15th EUROPT Workshop on Advances in Continuous Optimization

Montréal, Canada, 12 — 14 juillet 2017

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Plenary II

13 juil. 2017 08h30 – 09h30

Salle: Amphithéâtre Banque Nationale

Présidée par Fabian Bastin

1 présentation

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    08h30 - 09h30

    Inverse optimization: closed-form solutions, geometry, and goodness of fit

    • Timothy Chan, prés., Department of Mechanical & Industrial Engineering, Faculty of Applied Science & Engineering, University of Toronto, Toronto, ON, Canada

    In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this talk 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, rho, the coefficient of complementarity, has similar properties to R^2 from regression and is quasiconvex in the input data, leading to an intuitive geometric interpretation. While rho 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.

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