Methods of Optimization, 1988, 394 pp., ISBN 0-911575-02-2, $80.00
Comprehensive unified treatment of methods of optimization
and control: theory, algorithms and applications. Linear Programming, Dynamic
Programming, and Calculus of Variations and Optimal Control; incorporates
recent developments not hitherto available. Revised second Russian edition.
Authors are well-known Soviet specialists.
TABLE OF CONTENS
Preface ..... vii
CHAPTER 1. LINEAR PROGRAMMING ..... 1
1.1. The Simplex Method ..... 1
1.2. Duality Theory ..... 27
1.3. The Dual Simplex Method ..... 40
1.4. Transportation Problems ..... 54
CHAPTER 2. CONVEX PROGRAMMING ..... 74
2.1. Convex Sets and Functions ..... 74
2.2. The Kuhn-Tucker Theorem ..... 80
2.3. The Duality Theory ..... 88
2.4. The Algorithm for Solving the Quadratic Problem .....
98
CHAPTER 3. NONLINEAR PROGRAMMING ..... 117
3.1. The General Nonlinear Programming Problem ..... 117
3.2. The Unconstrained Minimum Problem ..... 120
3.3. The Constrained Minimum Problem ..... 127
3.4. Minimization of Functions under Inequality Constraints ..... 146
3.5. Nonsmooth Problems ..... 155
3.6. Vector (Multicriteria) Optimization ..... 174
CHAPTER 4. COMPUTATIONAL METHODS OF
NONLINEAR PROGRAMMING ..... 182
4.1. Search Methods ..... 183
4.2. The Minimization of Functions of One Variable ..... 201
4.3. Methods of Unconstrained Minimization ..... 210
4.4. Methods of Constrained Minimization ..... 225
CHAPTER 5. DYNAMIC PROGRAMMING ..... 236
5.1. A Resource Allocation Problem ..... 236
5.2. TheTime-Optimal Tooling of Parts on Two Lathes ..... 240
5.3. The Construction of the Shortest Path on a Network ..... 243
5.4. The Maximal Flow Problem ..... 246
5.5. A Network Planning Problem ..... 248
CHAPTER 6. CALCULUS OF VARIATIONS ..... 251
6.1. The Fundamental Problem of the Calculus of Variations ..... 251
6.2. The Method of Variations ..... 257
6.3. The Investigation of the Second Variation ..... 271
CHAPTER 7. OPTIMAL CONTROL THEORY
7.1. The Fundamental Problem of Optimal Control ..... 281
7.2. Pontryagin’s Maximum Principle ..... 286
7.3. Transversality Conditions ..... 297
7.4. The Maximum Principle: Applications ..... 310
7.5. The Optimization of Linear Systems ..... 321
7.6. The Optimal Control of Discrete Processes ..... 334
7.7. Optimization of Systems with Distributed Parameters ..... 346
7.8. Linear Differential Games ..... 350
Index ..... 361
Transliteration Table (Russian-English) ..... 365