Linear Optimization and Extensions
Subtitle: Problems and Solutions (Universitext)
Edition: 1 edition
Publisher: Springer
Published: June 27, 2001
Language: eng
Format: Paperback
Number of pages: 453
ISBN-13: 9783540417446
Subjects: Combinatorics & graph theory; Decision theory: general; Economic theory & philosophy; Linear Programming; Problems, exercises, etc; Mathematics; Science/Mathematics; Computer Science; Discrete Mathematics; Lineares Programmieren; Mathematics / Combinatorics; gemischt-ganzzahliges Programmieren; linear optimization; lineare Optimierung; mixed-integer programming; Mathematical optimization
First sentence: (i) To formulate LLI's problem denote by x1 the liters of bourbon and by x2 the liters of whiskey produced during the planning period.
Description: This book offers a comprehensive treatment of the exercises and case studies as well as summaries of the chapters of the book "Linear Optimization and Extensions" by Manfred Padberg. It covers the areas of linear programming and the optimization of linear functions over polyhedra in finite dimensional Euclidean vector spaces. Here are the main topics treated in the book: Simplex algorithms and their derivatives including the duality theory of linear programming. Polyhedral theory, pointwise and linear descriptions of polyhedra, double description algorithms, Gaussian elimination with and without division, the complexity of simplex steps. Projective algorithms, the geometry of projective algorithms, Newtonian barrier methods. Ellipsoids algorithms in perfect and in finite precision arithmetic, the equivalence of linear optimization and polyhedral separation. The foundations of mixed-integer programming and combinatorial optimization.