Mathematical programming. Theory and algorithms. Transl. from the French by Steven Vajda.

*(English)*Zbl 0602.90090
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.

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 |