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Lagrange Multipliers in Locally Convex Spaces

Author

Listed:
  • Mohammed Bachir

    (Université Paris 1 Panthéon-Sorbonne)

  • Joël Blot

    (Université Paris 1 Panthéon-Sorbonne)

Abstract

We give a general Lagrange multiplier rule for mathematical programming problems in a Hausdorff locally convex space. We consider infinitely many inequality and equality constraints. Our results gives in particular a generalisation of the result of Jahn (Introduction to the theory of nonlinear optimization, Springer, Berlin, 2007), replacing Fréchet-differentiability assumptions on the functions by the Gateaux-differentiability. Moreover, the closed convex cone with a nonempty interior in the constraints is replaced by a strictly general class of closed subsets introduced in the paper and called “admissible sets”. Examples illustrating our results are given.

Suggested Citation

  • Mohammed Bachir & Joël Blot, 2024. "Lagrange Multipliers in Locally Convex Spaces," Journal of Optimization Theory and Applications, Springer, vol. 201(3), pages 1275-1300, June.
    • Handle: RePEc:spr:joptap:v:201:y:2024:i:3:d:10.1007_s10957-024-02428-z
    DOI: 10.1007/s10957-024-02428-z
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    References listed on IDEAS

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    1. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    2. A. Jourani & L. Thibault, 1993. "Approximations and Metric Regularity in Mathematical Programming in Banach Space," Mathematics of Operations Research, INFORMS, vol. 18(2), pages 390-401, May.
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