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Inverse optimization for multi-objective linear programming

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Abstract

This paper generalizes inverse optimization for multi-objective linear programming where we are looking for the least problem modifications to make a given feasible solution a weak efficient solution. This is a natural extension of inverse optimization for single-objective linear programming with regular “optimality” replaced by the “Pareto optimality”. This extension, however, leads to a non-convex optimization problem. We prove some special characteristics of the problem, allowing us to solve the non-convex problem by solving a series of convex problems.

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Acknowledgements

This work was partially supported by the MSK Cancer Center Support Grant/Core Grant (P30 CA008748).

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Authors and Affiliations

  1. Department of Mathematics, University of Qom, Qom, Iran

    Mostafa Naghavi & Ali Asghar Foroughi

  2. Department of Medical Physics, Memorial Sloan Kettering Cancer Center, New York, NY, USA

    Masoud Zarepisheh

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  1. Mostafa Naghavi
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  2. Ali Asghar Foroughi
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  3. Masoud Zarepisheh
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Correspondence to Mostafa Naghavi.

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Naghavi, M., Foroughi, A.A. & Zarepisheh, M. Inverse optimization for multi-objective linear programming. Optim Lett 13, 281–294 (2019). https://doi.org/10.1007/s11590-019-01394-0

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