Linear and Nonlinear Optimization

Richard W. Cottle is a Professor Emeritus from the Department of Management Science and Engineering at Stanford University. He received the degrees of A.B. and A.M. from Harvard University and the Ph.D. from the University of California at Berkeley, all three in mathematics. Under the supervision of George B. Dantzig, Cottle wrote a dissertation in which the linear and nonlinear complementarity problems were introduced. Upon completion of his doctoral studies in Berkeley, Cottle became a member of the technical staff of Bell Telephone Laboratories in Holmdel, New Jersey. Two years later, he joined the operations research faculty at Stanford University where he remained until his retirement in 2005.For nearly 40 years at Stanford, Cottle taught at the undergraduate, master's, and doctoral levels in a variety of optimization courses including linear and nonlinear programming, complementarity and equilibrium programming, and matrix theory. (The present volume is an outgrowth of one such course.) Most of Cottle's research lies within these fields.A former Editor-in-Chief of the journals Mathematical Programming and Mathematical Programming Study, Richard Cottle is well known for The Linear Complementarity Problem, a Lanchester Prize winning monograph he co-authored with two of his former doctoral students, Jong-Shi Pang and Richard E. Stone. In retirement he remains active in research and writing.Mukund N. Thapa is the President & CEO of Optical Fusion, Inc., and President of Stanford Business Software, Inc. He received a bachelor of technology degree in metallurgical engineering from the Indian Institute of Technology, Bombay. His Bachelor's thesis was on operations research techniques in iron and steel making. Later he obtained M.S. and Ph.D. degrees in operations research from Stanford University in 1981. His Ph.D. thesis was concerned with developing specialized algorithms for solving largescale unconstrained nonlinear minimization problems. By profession he is a software developer who produces commercial software products as well as commercial-quality custom software. Since 1978, Dr. Thapa has been applying the theory of operations research, statistics, and computer science to develop efficient, practical, and usable solutions to a variety of problems.At Optical Fusion, Inc., Dr. Thapa architected the development of a multi-point videoconferencing system for use over all IP-based networks. He holds several patents in the area. The feature-rich system focuses primarily on the needs of users and allows corporate users to seamlessly integrate conferencingin everyday business interactions. At Stanford Business Software, Dr. Thapa, ensured that the company produces high-quality turnkey software for clients. His expert knowledge of user friendly interfaces, databases, computer science, and modular software design plays an important role in making the software practical and robust. His specialty is the application of numerical analysis methodology to solve mathematical optimization problems. An experienced modeler, he is often asked by clients to consult, prepare analyses, and to write position papers.At the Department of Management Science and Engineering, Stanford University, Dr. Thapa has taught graduate-level courses in mathematical programming computation and numerical methods of linear programming. He is best known for his books with George B. Dantzig: Linear Programming 1: Introduction and Linear Programming 2: Theory and Extensions.

• Chapter 1. LP Models and Applications.- Chapter 2. Linear Equations and Inequalities.- Chapter 3. The Simplex Algorithm.- Chapter 4. The Simplex Algorithm Continued.- Chapter 5. Duality and the Dual Simplex Algorithm.- Chapter 6. Postoptimality Analysis.- Chapter 7. Some Computational Considerations.- Chapter 8. NLP Models and Applications.- Chapter 9. Unconstrained Optimization.- Chapter 10. Descent Methods.- Chapter 11. Optimality Conditions.- Chapter 12. Problems with Linear Constraints.- Chapter 13. Problems with Nonlinear Constraints.- Chapter 14. Interior-Point Methods.

“The historical notes in the book are interesting and well placed. … The book’s list of important references is quite complete. … this book is destined to become a classic in the field for beginning graduate students in optimization.” (S. Zlobec, Mathematical Reviews, January, 2018)