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Normality and Uniqueness of Multipliers in Isoperimetric Control Problems

Author

Listed:
  • Jorge Becerril

    (Faculdade de Engenharia da Universidade do Porto)

  • Karla Cortez

    (Universidad Nacional Autónoma de México)

Abstract

In this paper, we introduce the notion of normality relative to a set of constraints in isoperimetric control problems and study its relationship with the classic notion of normality, as well as the existence and uniqueness of Lagrange multipliers satisfying the maximum principle. We show that this notion leads to characterizing the uniqueness of a given multiplier, which also turns out to be equivalent to a strict Mangasarian–Fromovitz condition (as in the finite-dimensional case). Finally, we show that, if the cost function is allowed to vary between those for which a solution to the constrained problem is given, then the set of multipliers associated with each of them is a singleton, if and only if a strong normality assumption holds.

Suggested Citation

  • Jorge Becerril & Karla Cortez, 2019. "Normality and Uniqueness of Multipliers in Isoperimetric Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 947-964, September.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:3:d:10.1007_s10957-019-01515-w
    DOI: 10.1007/s10957-019-01515-w
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    References listed on IDEAS

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    1. Jorge A. Becerril & Javier F. Rosenblueth, 2017. "The Importance of Being Normal, Regular and Proper in the Calculus of Variations," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 759-773, March.
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