Quasi-Newton methods for saddlepoints (Q762890)

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.