The second edition of this established textbook combines volumes 1 and 2 of the first edition. The presentation and theory in this new edition have been extended and improved, and a number of new developments are described including an extended treatment of linear programming and important recent advances in polynomial time algorithms. There are new sections on network programming, a subject of great practical importance, and on optimality conditions for constrained composite non-smooth optimization. Throughout the book the emphasis is on practicability, and a great deal of attention is given to methods which have proved reliable and efficient. The first edition included frequent worked examples and exercises which both illustrated and extended the text, and these have been augmented in this combined second edition.