Quasi-Newton methods for saddlepoints
type: Item
instance of: scholarly article
title: Quasi-Newton methods for saddlepoints
zbMATH Open document ID: 0558.65042
DOI: 10.1007/BF00942187
published in: Journal of Optimization Theory and Applications
publication date: 1985-01-01T00:00:00Z
review text: The well-known quadratically convergent methods of the Huang type [cf. \textit{H. Y. Huang}, ibid. 5, 405-423 (1970; Zbl 0184.202) and \textit{H. Y. Huang} and \textit{A. V. Levy}, ibid. 6, 269-282 (1970; Zbl 0187.404)] to maximize or minimize a function \(f: {\mathbb{R}}^ n\to {\mathbb{R}}\) are generalized to find saddlepoints of f. Furthermore, a procedure is derived which homes in on saddlepoints with prescribed inertia, i.e., with a given number of positive and negative eigenvalues in the Hessian matrix of f. Examples are presented to show that saddlepoints with different inertia can be calculated from the same starting vector.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 3890634
zbMATH Keywords: quasi-Newton methods
zbMATH Keywords: conjugate directions
zbMATH Keywords: conjugate gradients
zbMATH Keywords: saddlepoints
author: Friedrich W. Biegler-König
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3890634