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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.
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