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# Accession Number:

## AD0860841

# Title:

## Mathematical Programming for Constrained Minimal Problems. Part 2 - Sequential Conjugate Gradient - Restoration Algorithm,

# Descriptive Note:

# Corporate Author:

## RICE UNIV HOUSTON TX AERO-ASTRONAUTICS GROUP

# Report Date:

## 1969-01-01

# Pagination or Media Count:

##
45.0

# Abstract:

## The problem of minimizing a function fx subject to a constraint Px 0 is considered. Here, f is a scalar, x an n-vector, and P a q-vector. A sequential algorithm is presented, made up of the alternate succession of gradient phases and restoration phases. In the gradient phase, a nominal point x satisfying the constraint is assumed a displacement delta x leading from point x to a varied point y is determined such that the value of the function is reduced. The determination of the displacement delta x incorporates information at point x as well as information at the previous point x. In the restoration phase, a nominal point y not satisfying the constraint is assumed a displacement delta y leading from point y to a varied point x is determined such that the constraint is restored to a prescribed degree of accuracy. The restoration is done by requiring the least-square change of the coordinates. It is shown that the sequential algorithm possesses quadratic convergence in the neighborhood of the constrained minimum. In particular, for a quadratic function subject to a linear constraint, the algorithm yields the minimum point in no more than n-q iterations. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#