Mathematical programming. Theory and algorithms. Transl. from the French by Steven Vajda. (English) Zbl 0602.90090

Minoux, M.

A Wiley-Interscience Publication. Chichester etc.: John Wiley and Sons. XXVIII, 489 p. £34.95 (1986).

[For a review of the French original (1983) see Zbl 0546.90056.]
This book serves as a broad introduction to mathematical programming. It provides the necessary theoretical background of the various solution techniques, but the main emphasis is placed on algorithms. The author makes a real attempt to unify the various subjects of mathematical programming. Following the introductory chapter on fundamental concepts, Chapters 2-6 are devoted to linear and nonlinear programming in finite dimensions (linear programming, one-dimensional optimization, unconstrained optimization, constrained optimization). In constrained optimization separate chapters deal with primal and with dual methods. In Chapter 7 an introduction to integer programming is given. Chapter 8 discusses solution methods in large-scale programming, generalized linear programming as well as decomposition techniques. Chapter 9 deals with dynamic programming. Finally, in Chapter 10 optimization in infinite dimensions and applications of it are discussed in Chapter 10.

Reviewer: S.Schaible

MSC:

90-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
90C05	Linear programming
65K05	Numerical mathematical programming methods
90C06	Large-scale problems in mathematical programming
49-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control
90C30	Nonlinear programming
49M37	Numerical methods based on nonlinear programming
90C10	Integer programming
49M27	Decomposition methods

Keywords:

introduction; unconstrained optimization

Citations:

Zbl 0546.90056