Lagrange Multipliers and Eigenvalue Problems

Eberhard Zeidler
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Eberhard Zeidler: Sektion Mathematik

Chapter Chapter 43 in Nonlinear Functional Analysis and its Applications, 1985, pp 273-312 from Springer

Abstract: Abstract In this chapter we shall show what nondegeneracy condition is necessary to justify the Lagrange multiplier rule in the narrower sense for smooth side conditions. Moreover, we will interpret this condition geometrically and explain the connection with manifolds in B-spaces. In this connection, a generalization of the implicit function theorem is the focal point (Theorem 43.C). The central concepts are: (α) Tangent vector, tangent space, and submersion. (β) Regular point of a set. (γ) Manifold. (δ) Tangential mapping. (ε) Critical point of a functional.

Keywords: Lagrange Multiplier; Eigenvalue Problem; Tangent Space; Tangent Vector; Open Neighborhood (search for similar items in EconPapers)
Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-5020-3_8

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DOI: 10.1007/978-1-4612-5020-3_8

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