MULTIVARIABLE OPTIMIZATION WITH CONSTRAINTS
ABSTRACT
It has been proved that in non linear programming, there are five methods of solving multivariable optimization with constraints. In this project, the usefulness of some of these methods (Kuhn – Tucker conditions and the Lagrange multipliers) as regards quadratic programming is unveiled. Also, we found out how the other methods are used in solving constrained optimizations and all these are supported with examples to aid better understanding.
TABLE OF CONTENTS
Title Page
Approval page
Dedication
Acknowledgement
Abstract
Table of Contents
CHAPTER ONE
1.0 Introduction
1.1 Basic definitions
1.2 Layout of work
CHAPTER TWO
2.0 Introduction
2.1 Lagrange Multiplier Method
2.2 Kuhn Tucker Conditions
2.3 Sufficiency of the Kuhn-Tucker Conditions
2.4 Kuhn Tucker Theorems
2.5 Definitions – Maximum and minimum of a function
2.6 Summary
CHAPTER THREE
3.0 Introduction
3.1 Newton Raphson Method
3.2 Penalty Function
3.3 Method of Feasible Directions
3.4 Summary
CHAPTER FOUR
4.0 Introduction
4.1 Definition – Quadratic Programming
4.2 General Quadratic Problems
4.3 Methods
4.4 Ways/Procedures of Obtaining the optimal
Solution from the Kuhn-Tucker Conditions
method
4.4.1 The Two-Phase Method
4.4.2 The Elimination Method
4.5 Summary
CHAPTER FIVE
Conclusion
References