Introduction to Optimization

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Springer Science & Business Media, Apr 18, 2006 - Mathematics - 246 pages

This undergraduate textbook introduces students of science and engineering to the fascinating field of optimization. It is a unique book that brings together the subfields of mathematical programming, variational calculus, and optimal control, thus giving students an overall view of all aspects of optimization in a single reference. As a primer on optimization, its main goal is to provide a succinct and accessible introduction to linear programming, nonlinear programming, numerical optimization algorithms, variational problems, dynamic programming, and optimal control. Prerequisites have been kept to a minimum, although a basic knowledge of calculus, linear algebra, and differential equations is assumed.

 

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Contents

Linear Programming
23
The simplex method
30
Duality
42
Some practical issues
49
Integer programming
59
Nonlinear Programming
67
KarushKuhnTucker optimality conditions
79
Convexity
86
justification
153
Variational problems under integral and pointwise restrictions
160
Summary of restrictions for variational problems
168
Bellmans equation
178
Some basic ideas on the numerical approximation
185
Optimal Control
195
Pontryagins principle
204
Another format
224

Sufficiency of the KKT conditions
95
Duality and convexity
102
Introduction
111
Variational Problems and Dynamic Programming
137
Exercises
232
Index 241
240
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