Linear and Nonlinear Optimization, Second Edition

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 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. Linear And Nonlinear Optimization, Second Edition 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.--jacket. Optimization Models -- Fundamentals Of Optimization -- Representation Of Linear Constraints -- Geometry Of Linear Programming -- The Simplex Method -- Duality And Sensitivity -- Enhancements Of The Simplex Method -- Network Problems -- Computational Complexity Of Linear Programming -- Interior-point Methods Of Linear Programming -- Basics Of Unconstrained Optimization -- Methods For Unconstrained Optimization -- Low-storage Methods For Unconstrained Problems -- Optimality Conditions For Constrained Problems -- Feasible-point Methods -- Penalty And Barrier Methods. Igor Griva, Stephen G. Nash, Ariela Sofer. Includes Bibliographical References (p. 707-725) And Index. 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 Provides an introduction to the applications, theory, and algorithms of linear and nonlinear optimization. The emphasis is on practical aspects - discussing modern algorithms, as well as the influence of theory on the interpretation of solutions or on the design of software. The book includes several examples of realistic optimization models that address important applications. 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. The book is designed to be flexible. It has a modular structure, and uses consistent notation and terminology throughout. It can be used in many different ways, in many different courses, and at many different levels of sophistication The book is heavily and badly highlighted. There are pages with an X in a heavy marker that render these pages useless. I am pretty unhappy with the book it is extremely difficult to read because of these marks and the price I payed was quite high. I would have returned it if it was not for the hazard of dealing with shipping back and fore.