Accession Number : AD0860841
Title : Mathematical Programming for Constrained Minimal Problems. Part 2 - Sequential Conjugate Gradient - Restoration Algorithm,
Corporate Author : RICE UNIV HOUSTON TX AERO-ASTRONAUTICS GROUP
Personal Author(s) : Miele, A. ; Huang, H. Y. ; Heideman, J. C.
Report Date : 1969
Pagination or Media Count : 45
Abstract : The problem of minimizing a function f(x) subject to a constraint P(x) = 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