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
I Basics 1
1 Optimization Models 3
2 Fundamentals of Optimization 43
3 Representation of Linear Constraints 77
II Linear Programming 95
4 Geometry of Linear Programming 97
5 The Simplex Method 125
6 Duality and Sensitivity 173
7 Enhancements of the Simplex Method 213
8 Network Problems 271
9 Computational Complexity of Linear Programming 301
10 Interior-Point Methods for Linear Programming 319
III Unconstrained Optimization 355
11 Basics of Unconstrained Optimization 357
12 Methods for Unconstrained Optimization 401
13 Low-Storage Methods for Unconstrained Problems 451
IV Nonlinear Optimization 481
14 Optimality Conditions for Constrained Problems 483
15 Feasible-Point Methods 549
16 Penalty and Barrier Methods 601
V Appendices 659
A Topics from Linear Algebra 661
B Other Fundamentals 691
C Software 703
Bibliography 707
