Mathematical optimization procedures of operations research. (Mathematische Optimierungsverfahren des Operations Research.) (German) Zbl 1226.90001

Gerdts, Matthias; Lempio, Frank

De Gruyter Studium. Berlin: de Gruyter (ISBN 978-3-11-024994-1/pbk; 978-3-11-024998-9/ebook). ix, 527 p. (2011).

The intention of the authors when writing this textbook was to motivate the main approaches for solving important optimization problems in operations research, to describe their properties and basic justifications. For linear programming problems they describe the simplex algorithm, methods to avoid cycling, duality and sensitivity. The main described approaches for solving linear integer optimization problems are branch-and-bound and Gomory cuts. For optimization problems over graphs the network simplex algorithm as well as algorithms for the computation of shortest paths are included. Separation theorems, optimality conditions and the dual problem are main points in the chapter on convex (nondifferentiable) optimization. Sensitivity, necessary and sufficient optimality conditions are introduced for differentiable optimization. A large chapter is devoted to algorithms for nonlinear programming. This includes SQP algorithms, penalty methods and interior point algorithms. Bellman’s optimality principle, the discrete and the continuous maximum principle are topics in a chapter on discrete dynamic optimization. The textbook is concluded with basic results for evolutionary algorithms including convergence analysis. All topics are carefully described, illustrated with many complete calculated examples and a number of exercises at the end of each chapter. The textbook is good suited for getting a quick introduction into a large number of different optimization problems in operations research. The examples and exercises are very helpful, basic properties and proofs are carefully explained.

Reviewer: Stephan Dempe (Freiberg)

MSC:

90-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operations research and mathematical programming
90C05	Linear programming
90C08	Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
90C10	Integer programming
90C25	Convex programming

Keywords:

Textbook in optimization; linear programming; optimization over networks; solution algorithms

Software:

SODAS