Accession Number:

AD0737528

Title:

Algorithms for Min-Max Problems in Hilbert Spaces

Descriptive Note:

Doctoral thesis

Corporate Author:

ILLINOIS UNIV AT URBANA COORDINATED SCIENCE LAB

Personal Author(s):

Report Date:

1972-01-01

Pagination or Media Count:

62.0

Abstract:

The problem considered is the minimization of a functional in Hilbert spaces, where the functional being considered is the maximum of a set of N functionals for each point in the Hilbert space. Two algorithms are presented. One is a gradient, or steepest-descent method. The other is a Newton-Raphson method. It is shown that the two algorithms are to be used together. The steepest-descent method is to be used first and then the Newton-Raphson method. To use the Newton-Raphson method, convexity is assumed. Both the theoretical and the numerical aspects of the algorithms are discussed.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE