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

  • 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. Application to non-smooth optimal control problems are given.

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Metadaten
Author: Daniel WachsmuthORCiD, Gerd WachsmuthORCiD
URL:https://arxiv.org/pdf/2111.10238.pdf
Title of the source (English):arXiv
Document Type:Scientific journal article not peer-reviewed
Language:English
Year of publication:2021
Tag:Second-order optimality conditions; bang-bang control; sparse control; twice epi-differentiability
Number of pages:40
Faculty/Chair:Fakultät 1 MINT - Mathematik, Informatik, Physik, Elektro- und Informationstechnik / FG Optimale Steuerung
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