Optimisation [by D.M. Greig (London: Longman, 1980, 179 pp.)]

This book provides a compact survey of selected topics in NLP at an ideal level for advanced undergraduates, especially engineering students. There are a number of fine books on NLP but, to our knowledge, no text designed specifically for a one-semester course is quite as nice. The book consists of five chapters. In Chapter 1, the classical theory of optimization including convexity, Lagrange multipliers, and the Kuhn- Tucker conditions is presented. Chapter 2 examines methods for finding a minimum in the unconstrained case. Chapter 3 studies the theory behind linear programming and, of course, the simplex method. In Chapter 4, applications of linear programming such as the transportation problem, an allocation problem, and game theory are discussed. Finally, in Chapter 5, methods for solving constrained optimization problems are presented; projection methods, quadratic programming methods, penalty and barrier function methods, and Lagrangian methods are described in detail. The book is terse and suffers from a lack of illustrative examples. The instructor should planon providing motivation in order to overcome this limitation.