Abstract
The paper is devoted to the classical variational problem with a nonsmooth integrand of the functional to be minimized. The integrand is supposed to be subdifferentiable. Under some natural conditions the subdifferentiability of the functional considered is proved. The problem of finding the subdifferential descent direction is solved and the subdifferential descent method is applied to solve the original problem. The algorithm developed is demonstrated by examples.
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Acknowledgements
The author is sincerely grateful to his colleagues Maksim Dolgopolik and Grigoriy Tamasyan for numerous fruitful discussions and to the anonymous referee, whose comments helped to significantly improve the paper. The work was supported by the Russian Science Foundation (project no. 21-71-00021).
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Fominyh, A.V. The subdifferential descent method in a nonsmooth variational problem. Optim Lett 17, 675–698 (2023). https://doi.org/10.1007/s11590-022-01897-3
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DOI: https://doi.org/10.1007/s11590-022-01897-3