A GLOBALLY CONVERGENT LINEARLY CONSTRAINED LAGRANGIAN METHOD FOR NONLINEAR OPTIMIZATION

a dissertation

submitted to the department of management science and engineering and the committee on graduate studies

of stanford university

in partial fulfillment of the requirements

for the degree of doctor of philosophy

in

operations research

Michael P. Friedlander August 2002

Copyright \begin{matrix}c \\ ◯ \end{matrix} 2002 by Michael P. Friedlander All Rights Reserved

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Michael A. Saunders (Principal Advisor)

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Walter Murray

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Philip E. Gill

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

Gene H. Golub

Approved for the University Committee on Graduate Studies: iv

Abstract

Abstract goes here. vi

Acknowledgments

Achnowledgments go here. viii

Contents

List of Tables, Figures, and Algorithms xi 1 Introduction 1

1.1 A section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Augmented Lagrangian Methods 5 x

Tables, Figures, and Algorithms

Tables Figures

xii

Chapter 1 Introduction

This is Chapter 1.

2 Chapter 1 Introduction Here’s a new page just so you see what it looks like.

1.1 A section 3

1.1 A section

And here’s another.

4

Chapter 2 Augmented Lagrangian Methods

This is Chapter 2.

6

Bibilography

Bibliography goes here.