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Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales

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Abstract

We obtain Euler–Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and discrete settings: Our results seem new and interesting even in the particular cases when the time scale is the set of real numbers or the set of integers.

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Acknowledgements

This work was supported by FEDER funds through COMPETE—Operational Programme Factors of Competitiveness (“Programa Operacional Factores de Competitividade”) and by Portuguese funds through the Center for Research and Development in Mathematics and Applications (University of Aveiro) and the Portuguese Foundation for Science and Technology (“FCT—Fundação para a Ciência e a Tecnologia”), within project PEst-C/MAT/UI4106/2011 with COMPETE number FCOMP-01-0124-FEDER-022690. Torres was also supported by project PTDC/MAT/113470/2009.

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Authors and Affiliations

  1. Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

    Natália Martins & Delfim F. M. Torres

  2. Research Group on Mathematical Theory of Systems and Control, Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

    Natália Martins & Delfim F. M. Torres

Authors
  1. Natália Martins
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  2. Delfim F. M. Torres
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Correspondence to Delfim F. M. Torres.

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Communicated by Boris S. Mordukhovich.

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Martins, N., Torres, D.F.M. Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales. J Optim Theory Appl 155, 453–476 (2012). https://doi.org/10.1007/s10957-012-0065-y

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