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A Function Approximation Approach for Parametric Optimization

Author

Listed:
  • Alberto De Marchi

    (Universität der Bundeswehr München)

  • Axel Dreves

    (Universität der Bundeswehr München)

  • Matthias Gerdts

    (Universität der Bundeswehr München)

  • Simon Gottschalk

    (Universität der Bundeswehr München)

  • Sergejs Rogovs

    (Universität der Bundeswehr München)

Abstract

We present a novel approach for approximating the primal and dual parameter-dependent solution functions of parametric optimization problems. We start with an equation reformulation of the first-order necessary optimality conditions. Then, we replace the primal and dual solutions with some approximating functions and find for some test parameters optimal coefficients as solution of a single nonlinear least-squares problem. Under mild assumptions it can be shown that stationary points are global minima and that the function approximations interpolate the solution functions at all test parameters. Further, we have a cheap function evaluation criterion to estimate the approximation error. Finally, we present some preliminary numerical results showing the viability of our approach.

Suggested Citation

  • Alberto De Marchi & Axel Dreves & Matthias Gerdts & Simon Gottschalk & Sergejs Rogovs, 2023. "A Function Approximation Approach for Parametric Optimization," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 56-77, January.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:1:d:10.1007_s10957-022-02138-4
    DOI: 10.1007/s10957-022-02138-4
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    References listed on IDEAS

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    1. Axel Dreves, 2019. "An algorithm for equilibrium selection in generalized Nash equilibrium problems," Computational Optimization and Applications, Springer, vol. 73(3), pages 821-837, July.
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