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Directional derivatives of the solution of a parametric nonlinear program

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Abstract

Consider a parametric nonlinear optimization problem subject to equality and inequality constraints. Conditions under which a locally optimal solution exists and depends in a continuous way on the parameter are well known. We show, under the additional assumption of constant rank of the active constraint gradients, that the optimal solution is actually piecewise smooth, hence B-differentiable. We show, for the first time to our knowledge, a practical application of quadratic programming to calculate the directional derivative in the case when the optimal multipliers are not unique.

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Authors and Affiliations

  1. Department of Mathematics, University of Melbourne, 3052, Parkville, Vic., Australia

    D. Ralph

  2. Department of Mathematics, Technical University of Chemnitz, Germany

    S. Dempe

Authors
  1. D. Ralph
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  2. S. Dempe
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This author's research was supported by the Australian Research Council.

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Ralph, D., Dempe, S. Directional derivatives of the solution of a parametric nonlinear program. Mathematical Programming 70, 159–172 (1995). https://doi.org/10.1007/BF01585934

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  • DOI: https://doi.org/10.1007/BF01585934

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