GRADIENT-TYPE METHODS FOR UNCONSTRAINED OPTIMIZATION
By
Author
Presented To
Department of Mathematics
ABSTRACT
In this project, different gradient type methods which can be applied to
solve an unconstrained optimization problem have been investigated. This
project focuses on Barzilai and Borwein Gradient method, Monotone Gra-
dient method via weak secant equation and Monotone Gradient method via
Quasi-Cauchy Relation. Iterative scheme for each method was studied. To
apply each of these methods, the functions was assumed to be convex and
twice continuous differentiable. In yields of the application, a few stan-
dard unconstrained functions have been chosen for testing purposes. The
results obtained show the number of iterations used for getting an optimal
point. The result were used for analyzing the efficiency of the methods
studied. Two comparisons had been made in this project. First is the
Barzilai and Borwein Gradient method with Monotone Gradient method
via weak secant equation and the second is Barzilai and Borwein Gradi-
ent method with Monotone Gradient method via Quasi-Cauchy Relation.
These comparisons show that the Monotone Gradient type methods per-
form better as compared to the Barzilai and Borwein Gradient method.
The number of iterations clearly was not affected by the dimension. Fi-
nally, verification for the two proposed algorithms was done to show the
flow of the algorithms.
TABLE OF CONTENTS
TITLE i
DECLARATION OF ORIGINALITY ii
ACKNOWLEDGEMENTS vii
ABSTRACT viii
LIST OF FIGURES xi
LIST OF TABLES xii
CHAPTER 1 Introduction 1
1-1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1-2 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1-3 Problem Statement . . . . . . . . . . . . . . . . . . . . . 2
1-4 Research Methodology . . . . . . . . . . . . . . . . . . . 2
1-5 Methodology and Planning . . . . . . . .
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