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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