Daniel Wachsmuth ; Gerd Wachsmuth - Second-order conditions for non-uniformly convex integrands: quadratic growth in $L^1$

jnsao:8733 - Journal of Nonsmooth Analysis and Optimization, May 23, 2022, Volume 3 - https://doi.org/10.46298/jnsao-2022-8733
Second-order conditions for non-uniformly convex integrands: quadratic growth in $L^1$Article

Authors: Daniel Wachsmuth ; Gerd Wachsmuth ORCID

    We study no-gap second-order optimality conditions for a non-uniformly convex and non-smooth integral functional. The integral functional is extended to the space of measures. The obtained second-order derivatives contain integrals on lower-dimensional manifolds. The proofs utilize the convex pre-conjugate, which is an integral functional on the space of continuous functions. Applications to non-smooth optimal control problems are given.


    Volume: Volume 3
    Section: Original research articles
    Published on: May 23, 2022
    Accepted on: May 9, 2022
    Submitted on: November 22, 2021
    Keywords: Mathematics - Optimization and Control,49J53, 49J52, 49K30

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