DID YOU KNOW? DTIC has over 3.5 million final reports on DoD funded research, development, test, and evaluation activities available to our registered users. Click HERE
to register or log in.
Mathematical Programming for Constrained Minimal Problems. Part 2 - Sequential Conjugate Gradient - Restoration Algorithm,
RICE UNIV HOUSTON TX AERO-ASTRONAUTICS GROUP
Pagination or Media Count:
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
APPROVED FOR PUBLIC RELEASE