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Linear and nonlinear optimization

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This book introduces the applications, theory, and algorithms of linear and nonlinear optimization, with an emphasis on the practical aspects of the material. Its unique modular structure provides flexibility to accommodate the varying needs of instructors, students, and practitioners with different levels of sophistication in these topics. The succinct style of this second edition is punctuated with numerous real-life examples and exercises, and the authors include accessible explanations of topics that are not often mentioned in textbooks, such as duality in nonlinear optimization, primal-dual methods for nonlinear optimization, filter methods, and applications such as support-vector machines.

Part I of Linear and Nonlinear Optimization, Second Edition provides fundamentals that can be taught in whole or in part at the beginning of a course on either topic and then referred to as needed. Part II on linear programming and Part III on unconstrained optimization can be used together or separately, and Part IV on nonlinear optimization can be taught without having studied the material in Part II. In the preface the authors suggest course outlines that can be adjusted to the requirements of a particular course on both linear and nonlinear optimization, or to separate courses on these topics. Three appendices provide information on linear algebra, other fundamentals, and software packages for optimization problems. A supplemental website offers auxiliary data sets that are necessary for some of the exercises.

Audience: This book is primarily intended for use in linear and nonlinear optimization courses for advanced undergraduate and graduate students. It is also appropriate as a tutorial for researchers and practitioners who need to understand the modern algorithms of linear and nonlinear optimization to apply them to problems in science and engineering.

Contents: Preface; Part I: Basics; Chapter 1: Optimization Models; Chapter 2: Fundamentals of Optimization; Chapter 3: Representation of Linear Constraints; Part II: Linear Programming; Chapter 4: Geometry of Linear Programming; Chapter 5: The Simplex Method; Chapter 6: Duality and Sensitivity; Chapter 7: Enhancements of the Simplex Method; Chapter 8: Network Problems; Chapter 9: Computational Complexity of Linear Programming; Chapter 10: Interior-Point Methods of Linear Programming; Part III: Unconstrained Optimization; Chapter 11: Basics of Unconstrained Optimization; Chapter 12: Methods for Unconstrained Optimization; Chapter 13: Low-Storage Methods for Unconstrained Problems; Part IV: Nonlinear Optimization; Chapter 14: Optimality Conditions for Constrained Problems; Chapter 15: Feasible-Point Methods; Chapter 16: Penalty and Barrier Methods; Part V: Appendices; Appendix A: Topics from Linear Algebra; Appendix B: Other Fundamentals; Appendix C: Software; Bibliography; Index

Author(s): Igor Griva, Stephen G. Nash, Ariela Sofer
Edition: 2nd ed
Publisher: Society for Industrial and Applied Mathematics
Year: 2009

Language: English
Commentary: 61850
Pages: 766
City: Philadelphia

Contents......Page 7
Preface......Page 15
Part I - Basics......Page 25
Ch 1. Optimization Models......Page 27
Ch 2. Fundamentals of Optimization......Page 67
Ch 3. Representation of Linear Constraints......Page 101
Part II - Linear Programming......Page 119
Ch 4. Geometry of Linear Programming......Page 121
Ch 5. The Simplex Method......Page 149
Ch 6. Duality and Sensitivity......Page 197
Ch 7. Enhancements of the Simplex Method......Page 237
Ch 8. Network Problems......Page 295
Ch 9. Computational Complexity of Linear Programming......Page 325
Ch 10. Interior-Point Methods for Linear Programming......Page 343
Part III - Unconstrained Optimization......Page 379
Ch 11. Basics of Unconstrained Optimization......Page 381
Ch 12. Methods for Unconstrained Optimization......Page 425
Ch 13. Low-Storage Methods for Unconstrained Problems......Page 475
Part IV - Nonlinear Optimization......Page 505
Ch 14. Optimality Conditions for Constrained Problems......Page 507
Ch 15. Feasible-Point Methods......Page 573
Ch 16. Penalty and Barrier Methods......Page 625
Part V - Appendices......Page 683
Appendix A: Topics from Linear Algebra......Page 685
Appendix B: Other Fundamentals......Page 715
Appendix C: Software......Page 727
Bibliography......Page 731
Index......Page 751