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# Accession Number:

## AD0745958

# Title:

## Comparison of Several Gradient Algorithms for Mathematical Programming Problems

# Descriptive Note:

# Corporate Author:

## RICE UNIV HOUSTON TX AERO-ASTRONAUTICS GROUP

# Report Date:

## 1972-06-01

# Pagination or Media Count:

##
31.0

# Abstract:

## In the paper, the numerical solution of the basic problem of mathematical programming is considered. This is the problem of minimizing a function fx subject to a constraint phix 0. Here, f is a scalar, x an n- vector, and phi a q-vector, with qn. 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.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#