Nonlinear programming

The third edition of the book is a thoroughly rewritten version of the 1999 2nd edition. New material was included, some of the old material was discarded, and a large portion of the remainder was reorganized or revised. This book provides a comprehensive and accessible presentation of algorithms for solving continuous optimization problems. It relies on rigorous mathematical analysis, but also aims at an intuitive exposition that makes use of visualization where possible. It places particular emphasis on modern developments, and their widespread applications in fields such as large-scale resource allocation problems, signal processing, and machine learning. The book was developed through instruction at MIT, focuses on nonlinear and other types of optimization : iterative algorithms for constrained and unconstrained optimization, Lagrange multipliers and duality, large scale problems, and the interface between continuous and discrete optimization. Among its special features, the book : 1) provides extensive coverage of iterative optimization methods within a unifying framework ; 2) provides a detailed treatment of interior point methods for linear programming ; 3) covers in depth duality theory from both a variational and a geometrical / convex analysis point of view ; 4) includes much new material on a number of topics, such as neural network training, large-scale optimization, signal processing, machine learning, and optimal control ; 5) includes a large number of examples and exercises detailed solutions of many of which are posted on the internet.

"This is a thoroughly rewritten and substantially expanded edition of our best-selling nonlinear programming book. The treatment focuses on iterative algorithms for constrained and unconstrained optimization, Lagrange multipliers and duality, large scale problems, and the interfaces between continuous and discrete optimization. Among its special features, this edition of the book : provides extensive coverage of iterative optimization methods within a unifying framework ; covers in depth duality theory from both a variational and a geometric / convex analysis point of view ; provides a detailed treatment of interior point methods for linear programming ; includes much new material on a number of topics, such as neural network training, conic programming, proximal algorithms, and alternating direction methods of multipliers ; focuses on large-scale optimization topics of much current interest, such as incremental methods, and parallel and distributed computation, and their applications in machine learning and signal processing ; includes a large number of examples and exercises ; was developed through extensive classroom use in first-year graduate courses."--taken from back cover.

Chapter 1. Unconstrained optimization : Basic methods -- Chapter 2. Unconstrained optimization : Additional methods -- Chapter 3. Optimization over a convex set -- Chapter 4. Lagrange multiplier theory -- Chapter 5. Lagrange multiplier algorithms -- Chapter 6. Duality and convex programming -- Chapter 7. Dual methods -- Appendix A. Mathematical background -- Appendix B. Convex analysis -- Appendix C. Line search methods -- Appendix D. Implementation of Newton's method -- References -- Index.