By Alexander Schrijver
Conception of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This publication describes the idea of linear and integer programming and surveys the algorithms for linear and integer programming difficulties, targeting complexity research. It goals at complementing the extra virtually orientated books during this box. a different characteristic is the author's assurance of significant contemporary advancements in linear and integer programming. functions to combinatorial optimization are given, and the writer additionally contains broad ancient surveys and bibliographies. The ebook is meant for graduate scholars and researchers in operations study, arithmetic and laptop technology. it is going to even be of curiosity to mathematical historians. Contents 1 creation and preliminaries; 2 difficulties, algorithms, and complexity; three Linear algebra and complexity; four concept of lattices and linear diophantine equations; five Algorithms for linear diophantine equations; 6 Diophantine approximation and foundation relief; 7 primary recommendations and effects on polyhedra, linear inequalities, and linear programming; eight The constitution of polyhedra; nine Polarity, and blockading and anti-blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; eleven The simplex procedure; 12 Primal-dual, removal, and rest tools; thirteen Khachiyan's strategy for linear programming; 14 The ellipsoid approach for polyhedra extra often; 15 additional polynomiality ends up in linear programming; sixteen creation to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 absolutely unimodular matrices: basic houses and examples; 20 spotting overall unimodularity; 21 additional thought concerning overall unimodularity; 22 indispensable polyhedra and overall twin integrality; 23 slicing planes; 24 extra tools in integer linear programming; old and extra notes on integer linear programming; References; Notation index; writer index; topic index
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