Accession Number : AD0659294

Title :   FUNCTION MINIMIZATION WITHOUT DERIVATIVES BY A SEQUENCE OF QUADRATIC PROGRAMMING PROBLEMS.

Descriptive Note : Technical rept.,

Corporate Author : HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS

Personal Author(s) : Winfield,David H.

Report Date : AUG 1967

Pagination or Media Count : 22

Abstract : An algorithm is described for minimizing an arbitrary scalar cost function c(x) with respect to an n-vector x. At each stage of the minimization, the cost function is approximated by a quadratic form in the region about the current lowest-cost point. The next trial point is taken as the minimum of this quadratic form within a hypercube in n-space centered at the current lowest-cost point. The procedure has quadratic convergence, but differs from other quadratically convergent minimization algorithms in that (1) minimization is over a sequence of n-dimensional regions rather than over a sequence of one-dimensional straight lines (2) the local approximation to the cost surface need not be positive definite (3) each approximation depends only on true cost values and is independent of prior approximations (4) after each evaluation of cost at a trial point, the trial point is added, and a point distant from the current lowest-cost point is deleted, from the set of points to which the next quadratic form will interpolate. The algorithm takes relatively large steps, and is forced by (4) to learn from its failures. Test results are presented for N - 2 using Rosenbrock's parabolic valley as the cost function. (Author)

Descriptors :   (*QUADRATIC PROGRAMMING, OPTIMIZATION), (*COSTS, MATHEMATICAL MODELS), ALGORITHMS, NONLINEAR PROGRAMMING, MATHEMATICAL PROGRAMMING, CONVERGENCE

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE