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arXiv · 2111.10238

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

Daniel Wachsmuth·Gerd Wachsmuth
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Abstract

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.

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Daniel Wachsmuth, Gerd Wachsmuth. 2021-11-19. Second-order conditions for non-uniformly convex integrands: quadratic growth in $L^1$. https://doi.org/10.46298/jnsao-2022-8733

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