Constrained Optimization in the Calculus of Variations and Optimal Control Theory / Edition 1

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A major problem in current applied mathematics is the lack of efficient and accurate techniques to solve optimization problems in the calculus of variations and optimal control theory. This is surprising since problems occur throughout many areas of applied mathematics, engineering, physical sciences, economics, and biomedicine. For instance, these techniques are used to solve rocket trajectory problems, current flow problems in electronics manufacturing, and financial risk problems in investing. The authors have written a unique book to remedy this problem. The first half of the book contains classical material in the field, the second half unique theoretical and numerical methods for constrained problems.
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Editorial Reviews

Offers new ways to obtain analytical and numerical results with methods developed by the authors, along with classical techniques for constrained problems. The introduction gives a solid grounding in nonlinear programming, the calculus of variations, and optimal control theory. A wide range of applications is shown, including rocket trajectory, current flow in electronics, manufacturing, and financial risks in investing. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780442007225
  • Publisher: CRC Press
  • Publication date: 9/28/1992
  • Edition number: 1
  • Pages: 224
  • Product dimensions: 8.14 (w) x 7.80 (h) x 0.60 (d)

Table of Contents

1 The Finite Dimensional Problem 1
1.1 The Free Problem 2
1.2 The Equality Constrained Problem 6
1.3 The Inequality Constrained Problem 12
1.4 Newton's Method 19
2 The Basic Theory of the Calculus of Variations 23
2.1 Introduction 24
2.2 Some Examples 26
2.3 Critical Point Conditions 33
2.4 Additional Necessary Conditions 49
3 Additional Topics 61
3.1 Miscellaneous Results 61
3.2 Sufficiency Theory 67
3.3 Several Dependent Variables 76
4 Optimal Control 83
4.1 A Basic Problem 84
4.2 The Minimal Time Problem: An Example of Abnormality 99
5 Unconstrained Reformulations 105
5.1 The Optimal Control Problems 106
5.2 Constrained Calculus of Variations Problems 115
5.3 Kuhn-Tucker Reformulation 121
6 Numerical Theory. Methods and Results 129
6.1 The Basic Problem in Calculus of Variations 131
6.2 Numerical Transversality Conditions for General Problems 149
6.3 Kuhn-Tucker Method 165
6.4 Higher Order Algorithm 168
6.5 Partial Differential Equations 174
Appendix A: Detailed References 191
Appendix B: Uses of This Book 197
Appendix C: Additional Problems 199
References 211
Index 215
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