Comparison of Several Gradient Algorithms for Mathematical Programming Problems

Abstract

In the paper, the numerical solution of the basic problem of mathematical programming is considered. This is the problem of minimizing a function f(x) subject to a constraint phi(x) = 0. Here, f is a scalar, x an n- vector, and phi a q-vector, with q<n. Six variations of the sequential gradient-restoration algorithm and the combined gradient-restoration algorithm are considered, and their relative efficiency (in terms of number of iterations for convergence) is evaluated. The variations being considered are as follows: (i) SGRA-CR, sequential gradient-restoration algorithm, complete restoration, (ii) SGRA-IR, sequential gradient-restoration algorithm, incomplete restoration, (iii) SGRA-OR, sequential gradient-restoration algorithm, optional restoration, (iv) CGRA-NR, combined gradient-restoration algorithm, no restoration, (v) CGRA- AR, combined gradient-restoration algorithm, alternate restoration, (vi) CGRA- OR, combined gradient-restoration algorithm, optional restoration.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1972
Accession Number
AD0745958

Entities

People

  • A. V. Levy
  • Angelo Miele
  • J. L. Tietze

Organizations

  • Rice University

Tags

Communities of Interest

  • C4I
  • Space

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Astronautics
  • Computer Programming
  • Convergence
  • Displacement
  • Efficiency
  • Electrical Engineering
  • Engineering
  • Errors
  • Inequalities
  • Iterations
  • Mathematical Programming
  • Scientific Research
  • United States
  • Universities

Readers

  • Analytical Mechanics
  • Operations Research