Applied Nonlinear Programming
Copyright © 2006, New Age International (P) Ltd., Publishers
Published by New Age International (P) Ltd., Publishers
PREFACE
In most of the practical situations, the objective function and/
or constraints are nonlinear. The solution methods to deal
with such problems may be called as nonlinear programming.
The present book is focussed on applied nonlinear programming.
A general introduction is provided discussing various
industrial/managerial applications. Convex and concave
functions are explained for single variaSble and multi-variable
examples. As a special case of nonlinear programming,
geometric programming is also discussed. It is expected that
the book will be a useful reference/text for professionals/students
of engineering and management disciplines including operations
research.
Dr. SANJAY SHARMA
CONTENTS
Preface v
1. Introduction 1
1.1 Applications 1
1.2 Maxima and Minima 7
1.3 Convex and Concave Function 8
1.4 Classification 12
2. One Variable Optimization 16
2.1 Unrestricted Search 17
2.2 Method of Golden Section 21
2.3 Quadratic Interpolation 27
2.4 Newton Raphson Method 29
3. Unconstrained and Constrained
Optimization 32
3.1 Dichotomous Search 33
3.2 Univariate Method 35
3.3 Penalty Function Method 39
3.4 Industrial Application 41
4. Geometric Programming 47
4.1 Introduction 47
4.2 Mathematical Analysis 49
4.3 Examples 52
5. Multi-Variable Optimization 60
5.1 Convex/Concave Function 60
5.2 Lagrangean Method 66
5.3 The Kuhn-Tucker Conditions 70
5.4 Industrial Economics Application 74
5.5 Inventory Application 77
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