DID YOU KNOW? DTIC has over 3.5 million final reports on DoD funded research, development, test, and evaluation activities available to our registered users. Click

HERE to register or log in.

# Accession Number:

## AD0720835

# Title:

## Mathematical Programming for Constrained Minimal Problems. Part 3. Combined Gradient-Restoration Algorithm,

# Descriptive Note:

# Corporate Author:

## RICE UNIV HOUSTON TEX AERO-ASTRONAUTICS GROUP

# Report Date:

## 1970-01-01

# Pagination or Media Count:

##
27.0

# Abstract:

## The problem of minimizing a function fx subject to a constraint phix O is considered. Here, f is a scalar, x an n-vector, and phi a q-vector. A combined gradient-restoration algorithm is presented this is an iterative algorithm characterized by a displacement delta x leading toward the minimum point while simultaneously leading toward constraint satisfaction. This displacement, generated by minimizing the first-order change of the function subject to the constraint employed in linearized form and a quadratic constraint on delta x, has the direction of the gradient of the augmented function Fx, lambda fx lambda sup Tphix. The descent properties of the algorithm are studied, and schemes to determine the optimum stepsize are discussed. Three numerical examples are presented. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#