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

Personal Author(s):

• Miele, A.
• Huang, H. Y.
• Heideman, J. C.

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

Descriptors:

• (*MATHEMATICAL PROGRAMMING
• OPTIMIZATION)
• ITERATIONS
• ALGORITHMS

Subject Categories:

• Operations Research

Distribution Statement:

APPROVED FOR PUBLIC RELEASE