
Accession Number : AD0747277
Title : Computational Algorithm for Unconstrained Minimization.
Descriptive Note : Doctoral thesis,
Corporate Author : AIR FORCE INST OF TECH WRIGHTPATTERSON 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 FletcherPowell. 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