
Accession Number : AD0860841
Title : Mathematical Programming for Constrained Minimal Problems. Part 2  Sequential Conjugate Gradient  Restoration Algorithm,
Corporate Author : RICE UNIV HOUSTON TX AEROASTRONAUTICS 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 nvector, and P a qvector. 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 leastsquare 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 nq iterations. (Author)
Descriptors : (*MATHEMATICAL PROGRAMMING, OPTIMIZATION), ITERATIONS, ALGORITHMS.
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE