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.

https://doi.org/10.46298/jnsao-2022-8733
Source: arXiv.org:2111.10238
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
Licence: Attribution-Non Commercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
Funding:
    Source : OpenAIRE Graph
  • Non-smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization; Funder: Deutsche Forschungsgemeinschaft; Code: 274039581/SPP 1962

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