Vanderplaats-toc - CONTENTS Chapter 1 BASIC CONCEPTS 1-1...

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i Chapter 1 BASIC CONCEPTS 1 1-1 INTRODUCTION 1 1-2 OPTIMIZATION CONCEPTS 4 1-3 GENERAL PROBLEM STATEMENT 10 1-4 THE ITERATIVE OPTIMIZATION PROCEDURE 11 1-5 EXISTENCE AND UNIQUENESS OF AN OPTIMUM SOLUTION 14 1-5.1 Unconstrained Problems 14 1-5.2 Constrained Problems 16 1-5.3 The Kuhn-Tucker Conditions 20 1-6 CONCLUDING REMARKS 26 1-6.1 Advantages of Numerical Optimization 27 1-6.2 Limitations of Numerical Optimization 27 1-6.3 Summary 28 REFERENCES 28 PROBLEMS 29 Chapter 2 FUNCTIONS OF ONE VARIABLE 32 2-1 INTRODUCTION 32 2-2 POLYNOMIAL APPROXIMATIONS 34 2-2.1 Polynomial Coefficients 38 2-2.2 The Zero of a Polynomial 41 2-2.3 The Minimum or Maximum of a Polynomial 46 2-3 GOLDEN SECTION METHOD 53 2-3.1 The Golden Section Algorithm 57 2-3.2 The Maximum or Zero of a Function 61 2-4 FINDING BOUNDS ON THE SOLUTION 64 2-4.1 Bounds on F = 0 65 2-4.2 Bounds on the Minimum of F 66 CONTENTS
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CONTENTS ii 2-5 CONSTRAINED FUNCTIONS OF ONE VARIABLE 70 2-5.1 The Direct Approach 71 2-5.2 The Indirect Approach 73 2-6 A GENERAL STRATEGY FOR MINIMIZING FUNCTIONS OF ONE VARIABLE 75 2-6.1 Unconstrained Functions 76 2-6.2 Constrained Functions – Initially Feasible 77 2-6.3 Constrained Functions – Initially Infeasible 80 2-7 SUMMARY 82 REFERENCES 82 PROBLEMS 86 Chapter 3 UNCONSTRAINED FUNCTIONS OF N VARIABLES 90 3-1 INTRODUCTION 90 3-1.1 Search Methods 93 3-1.2 General Optimization Strategy 95 3-1.3 The Optimization Algorithm 99 3-2 ZERO-ORDER METHODS 100 3-2.1 Random Search 100 3-2.2 Powell's Method 104 3-2.3 Other Zero-Order Methods 109 3-3 FIRST-ORDER METHODS
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This note was uploaded on 06/06/2011 for the course EAS 4240 taught by Professor Peterifju during the Spring '08 term at University of Florida.

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Vanderplaats-toc - CONTENTS Chapter 1 BASIC CONCEPTS 1-1...

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