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Inverse Linear Programming

In: Recent Advances in Optimization

Author

Listed:
  • Stephan Dempe

    (Technical University Bergakademie Freiberg)

  • Sebastian Lohse

    (Technical University Bergakademie Freiberg)

Abstract

Summary Let Ψ(b, c) be the solution set mapping of a linear parametric optimization problem with parameters b in the right hand side and c in the objective function. Then, given a point x0 we search for parameter values b̄ and c̄ as well as for an optimal solution x̄ ∈ Ψ (b̄, c̄) such that ‖x̄ − x0‖ is minimal. This problem is formulated as a bilevel programming problem. Focus in the paper is on optimality conditions for this problem. We show that, under mild assumptions, these conditions can be checked in polynomial time.

Suggested Citation

  • Stephan Dempe & Sebastian Lohse, 2006. "Inverse Linear Programming," Lecture Notes in Economics and Mathematical Systems, in: Alberto Seeger (ed.), Recent Advances in Optimization, pages 19-28, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-28258-7_2
    DOI: 10.1007/3-540-28258-0_2
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    Citations

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    Cited by:

    1. András Kovács, 2021. "Inverse optimization approach to the identification of electricity consumer models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 521-537, June.
    2. Ghobadi, Kimia & Mahmoudzadeh, Houra, 2021. "Inferring linear feasible regions using inverse optimization," European Journal of Operational Research, Elsevier, vol. 290(3), pages 829-843.
    3. Chow, Joseph Y.J. & Recker, Will W., 2012. "Inverse optimization with endogenous arrival time constraints to calibrate the household activity pattern problem," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 463-479.
    4. Sanjay Mehrotra & Kibaek Kim, 2011. "Outcome based state budget allocation for diabetes prevention programs using multi-criteria optimization with robust weights," Health Care Management Science, Springer, vol. 14(4), pages 324-337, November.
    5. Jonathan Yu-Meng Li, 2021. "Inverse Optimization of Convex Risk Functions," Management Science, INFORMS, vol. 67(11), pages 7113-7141, November.

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