Algorithms for Min-Max Problems in Hilbert Spaces

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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1972
Accession Number
AD0737528

Entities

People

  • Robert W. Hecht

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Computers
  • Differential Equations
  • Digital Computers
  • Electrical Engineering
  • Engineering
  • Equations
  • Equations Of State
  • Hilbert Space
  • Illinois
  • Integral Equations
  • Riccati Equation
  • Sequences
  • Steepest Descent Method
  • Systems Engineering
  • Systems Science

Readers

  • Calculus or Mathematical Analysis
  • Operations Research

Technology Areas

  • Space