Accession Number : AD0747277
Title : Computational Algorithm for Unconstrained Minimization.
Descriptive Note : Doctoral thesis,
Corporate Author : AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OHIO SCHOOL OF ENGINEERING
Personal Author(s) : Kujawski,Bruce T.
Report Date : MAR 1972
Pagination or Media Count : 63
Abstract : A generalized descent algorithm theory is developed for unconstrained minimization problems. Here a descent algorithm is defined as a computational procedure where at each iteration a descent direction is determined and a single dimensional search is made for the minimum in the descent direction. The theory is shown to be a generalization of the three most common descent algorithms; gradient, conjugate gradient and Fletcher-Powell. Since execution of the single dimensional search can be computationally time consuming, two additional algorithms are presented which reduce or eliminate single dimensional search time. The first is a modification of Davidon's Variance Algorithm and requires a minimal single dimensional search. The second is a direct method for minimizing a special class of quadratic functions. (Author)
Descriptors : (*FUNCTIONS(MATHEMATICS), OPTIMIZATION), STEEPEST DESCENT METHOD, HILBERT SPACE, ITERATIONS, COMPUTER PROGRAMMING, MATRICES(MATHEMATICS), THESES
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE