The 5th edition of this classic textbook covers the central concepts of practical optimization techniques with an emphasis on methods that are both stateoftheart and popular. One major insight is the connection between the purely analytical character of an optimization problem and the behavior of algorithms used to solve that problem. Endofchapter exercises are provided for all chapters. ampnbspThe material is organized into three separate parts. Part I offers a selfcontained introduction to linear programming. The presentation in this part is fairly conventional covering the main elements of the underlying theory of linear programming many of the most effective numerical algorithms and many of its important special applications. Part II which is independent of Part I covers the theory of unconstrained optimization including both derivations of the appropriate optimality conditions and an introduction to basic algorithms. This part of the book explores the general properties of algorithms and defines various notions of convergence. In turn Part III extends the concepts developed in the second part to constrained optimization problems. Except for a few isolated sections this part is also independent of Part I. As such Parts II and III can easily be used without reading Part I and in fact the book has been used in this way at many universities. ampnbspNew to this edition are popular topics in data science and machine learning such as the Markov Decision Process Farkas lemma convergence speed analysis duality theories and applications various firstorder methods stochastic gradient method mirrordescent method FrankWolf method ALMADMM method interior trustregion method for nonconvex optimization distributionally robust optimization online linear programming semidefinite programming for sensornetwork localization and infeasibility detection for nonlinear optimization.