Accession Number : AD0720835

Title :   Mathematical Programming for Constrained Minimal Problems. Part 3. Combined Gradient-Restoration Algorithm,

Corporate Author : RICE UNIV HOUSTON TEX AERO-ASTRONAUTICS GROUP

Personal Author(s) : Miele,A. ; Heideman,J. C. ; Levy,A. V.

Report Date : 1970

Pagination or Media Count : 27

Abstract : The problem of minimizing a function f(x) subject to a constraint phi(x) = O is considered. Here, f is a scalar, x an n-vector, and phi a q-vector. A combined gradient-restoration algorithm is presented: this is an iterative algorithm characterized by a displacement delta x leading toward the minimum point while simultaneously leading toward constraint satisfaction. This displacement, generated by minimizing the first-order change of the function subject to the constraint employed in linearized form and a quadratic constraint on delta x, has the direction of the gradient of the augmented function F(x, lambda)= f(x) +(lambda sup T)phi(x). The descent properties of the algorithm are studied, and schemes to determine the optimum stepsize are discussed. Three numerical examples are presented. (Author)

Descriptors :   (*MATHEMATICAL PROGRAMMING, ALGORITHMS), MINIMAX TECHNIQUE, ITERATIONS, MATRICES(MATHEMATICS), INEQUALITIES, CONVERGENCE

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE