Davidon'S Method in Hilbert Space.

摘要

An extension of Davidon's method from an N-dimensional Euclidean vector space to a real Hilbert space X is presented, and the convergence of the iterations is established. The conjugate gradient and steepest descent methods, which have previously been studied in Hilbert spaces are included to indicate the similarity with the method discussed. Finally a control problem with linear dynamics and quadratic costs is considered in the framework of these iterations. (Author)