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  1. Home > Articles & Issues >
  2. Articles >
  3. Second-order conditi ...
Article

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

Daniel Wachsmuth, Gerd Wachsmuth ORCID
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Submitted on
November 22, 2021
Accepted on
May 9, 2022
Published on
May 23, 2022
Last modified on
March 31, 2025
Volume 3
Volume 3
Original research articles
DOI
10.46298/jnsao-2022-8733
License
Attribution-Non Commercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
Deutsche Forschungsgemeinschaft
274039581/SPP 1962
Non-smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization
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883
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615
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Second-order conditions for non-uniformly convex integrands: quadratic growth in $L^1$

Daniel Wachsmuth, Gerd Wachsmuth ORCID
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.
Keywords
  • Mathematics - Optimization and Control
  • 49J53, 49J52, 49K30
Mathematics Subject Classification 2020
  • 49J52 - Nonsmooth analysis
  • 49J53 - Set-valued and variational analysis
  • 49K30 - Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
Linked publications - datasets - software
  • Has review

    Review available on zbMATH Open, by Mohammad Hossein Alizadeh (Zanjan) (English)

Cited by

Source: OpenCitations

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