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

DOI10.46298/JNSAO-2022-8733arXiv2111.10238MaRDI QIDQ6383466

Publication date: 19 November 2021

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.

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Set-valued and variational analysis (49J53) Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49K30)

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