
Accession Number : AD0720835
Title : Mathematical Programming for Constrained Minimal Problems. Part 3. Combined GradientRestoration Algorithm,
Corporate Author : RICE UNIV HOUSTON TEX AEROASTRONAUTICS 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 nvector, and phi a qvector. A combined gradientrestoration 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 firstorder 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