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Optimality Conditions for Discrete-Time Control Problems

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Abstract

We consider an optimal control problem governed by a system of nonlinear difference equations. We obtain the existence of the optimal control as well as first-order optimality conditions of Pontryagin type by using the Dubovitskii–Milyutin formalism. Also, we give the necessary and sufficient conditions for global optimality.

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Acknowledgements

The authors are grateful to anonymous referees for many comments and suggestions which improved the quality of the paper. This research has been partially supported by MTM2015-66185 (MINECO/FEDER, UE) and V. Vivanco-Orellana was supported by Dirección de Investigación e Innovación DIN 05/2015, UCSC-Chile.

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Authors and Affiliations

  1. Departamento de Matemática, Universidad de Tarapacá, Casilla 7D, Arica, Chile

    Marko Antonio Rojas-Medar

  2. Departamento de Matemática, Universidade Tecnológica Federal do Paraná, Curitiba, PR, Brazil

    Camila Isoton

  3. Departamento de Matemática, Universidade Federal do Paraná, Curitiba, PR, Brazil

    Lucelina Batista dos Santos

  4. Departamento de Matemática, Universidad Católica de la Santísima Concepción, Concepción, Chile

    Violeta Vivanco-Orellana

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  1. Marko Antonio Rojas-Medar
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  2. Camila Isoton
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  3. Lucelina Batista dos Santos
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  4. Violeta Vivanco-Orellana
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Correspondence to Marko Antonio Rojas-Medar.

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Communicated by Boris S. Mordukhovich.

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Rojas-Medar, M.A., Isoton, C., dos Santos, L.B. et al. Optimality Conditions for Discrete-Time Control Problems. J Optim Theory Appl 185, 115–133 (2020). https://doi.org/10.1007/s10957-020-01638-5

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