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Optimality Conditions for Linear-Convex Optimal Control Problems with Mixed Constraints

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Abstract

In this paper, we provide sufficient optimality conditions for convex optimal control problems with mixed constraints. On one hand, the data delimiting the problem we consider is continuous and jointly convex on the state and control variables, but on the other hand, smoothness on the data of the problem, on the candidate to minimizer and/or on the multipliers is not needed. We also show that, under a suitable interior feasibility condition, the optimality conditions are necessary as well and can be written as a Maximum Principle in normal form. The novelty of this last part is that no additional regularity conditions on the mixed constraints, such as the Mangasarian–Fromovitz constraint qualification or the bounded slope condition, are required. A discussion about the regularity of the costate is also provided.

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Notes

  1. It is important to highlight that in [16, Hypotheses 2.2] the upper semicontinuity is understood in the same sense as in [28], that is, the multifunctions have closed graphs.

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Acknowledgements

J. Becerril was supported by CONICYT-PIA Basal Program CMM-AFB170001, and C. Hermosilla was supported by ANID-Chile through FONDECYT Grant Number 11190456.

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Authors and Affiliations

  1. Departamento de Ingeniería y Ciencias, Instituto Tecnológico y de Estudios Superiores de Monterrey, Monterrey, Estado de México, Mexico

    Jorge Becerril

  2. Departamento de Matemática, Universidad Técnica Federico Santa María, Valparaiso, Chile

    Cristopher Hermosilla

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  1. Jorge Becerril
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  2. Cristopher Hermosilla
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Correspondence to Cristopher Hermosilla.

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Communicated by Aram Arutyunov.

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Becerril, J., Hermosilla, C. Optimality Conditions for Linear-Convex Optimal Control Problems with Mixed Constraints. J Optim Theory Appl 194, 795–820 (2022). https://doi.org/10.1007/s10957-022-02049-4

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