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:

1972-03-01

Pagination or Media Count:

63.0

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 Davidons 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