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Differentiability with respect to parameters of solutions to convex programming problems

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Abstract

We consider a family of convex programming problems that depend on a vector parameter, characterizing those values of parameters at which solutions and associated Lagrange multipliers are Gâteaux differentiable.

These results are specialized to the problem of the metric projection onto a convex set. At those points where the projection mapping is not differentiable the form of Clarke's generalized derivative of this mapping is derived.

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Authors and Affiliations

  1. Systems Research Institute of the Polish Academy of Sciences, ul. Newelska 6, 01-447, Warszawa, Poland

    Kazimierz Malanowski

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  1. Kazimierz Malanowski
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Malanowski, K. Differentiability with respect to parameters of solutions to convex programming problems. Mathematical Programming 33, 352–361 (1985). https://doi.org/10.1007/BF01584382

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  • DOI: https://doi.org/10.1007/BF01584382

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