Mathematical Programming for Constrained Minimal Problems. Part 2 - Sequential Conjugate Gradient - Restoration Algorithm,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1969
- Accession Number
- AD0860841
Entities
People
- Angelo Miele
- H. Y. Huang
- J. C. Heideman
Organizations
- Rice University