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On the existence of Lagrange multipliers in nonlinear programming in Banach spaces

  • Part 1: Optimization
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Optimization and Optimal Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 30))

Abstract

The existence of Lagrange-Karush-Kuhn-Tucker multipliers in differentiable mathematical programming is shown to be a direct consequence of fundamental rules for computing tangent cones. The relationships of these rules with the transversality conditions of differential topology are pointed out. These rules also bear some connections with subdifferential calculus for convex (or tangentially convex [20]) functions.

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Authors and Affiliations

  1. Departement de Mathématiques, Faculté des Sciences Avenue Philippon, 64000, PAU, France

    Jean-Paul Penot

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  1. Jean-Paul Penot
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Alfred Auslender Werner Oettli Josef Stoer

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© 1981 Springer-Verlag

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Penot, JP. (1981). On the existence of Lagrange multipliers in nonlinear programming in Banach spaces. In: Auslender, A., Oettli, W., Stoer, J. (eds) Optimization and Optimal Control. Lecture Notes in Control and Information Sciences, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0004508

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  • DOI: https://doi.org/10.1007/BFb0004508

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10627-2

  • Online ISBN: 978-3-540-38591-2

  • eBook Packages: Springer Book Archive

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