Author(s): Shmuel Onn
Series: Zurich Lectures in Advanced Mathematics 7
Publisher: European Mathematical Society
Year: 2010
Language: English
Pages: 147
Preface......Page 7
Contents......Page 9
Introduction......Page 11
Outline of the monograph......Page 12
Nonlinear matroid problems......Page 14
Nonlinear multicommodity flows......Page 17
Complexity......Page 21
Finiteness......Page 22
Convex Discrete Maximization......Page 24
Image and fibers......Page 25
Small radius and weight......Page 28
Edge directions and zonotopes......Page 33
Efficient convex maximization......Page 36
Small radius and weight revisited......Page 38
Totally unimodular systems......Page 39
Convex combinatorial maximization......Page 41
Quadratic binary programming......Page 43
Matroids and matroid intersections......Page 44
Vector partitioning and clustering......Page 46
Graver bases......Page 50
Efficient separable convex minimization......Page 53
Distance minimization......Page 58
Convex integer maximization......Page 59
Weighted separable convex minimization......Page 60
Totally unimodular systems revisited......Page 61
Bounds on Graver bases......Page 62
n-Fold Integer Programming......Page 64
Graver bases of n-fold products......Page 65
Efficient n-fold integer programming......Page 68
Nonlinear many-commodity transshipment......Page 72
Nonlinear multicommodity transportation......Page 73
Stochastic integer programming......Page 75
Graver approximation scheme......Page 81
Multiway Tables and Universality......Page 84
The universality theorem......Page 86
Multiindex transportation problems......Page 90
Privacy in statistical databases......Page 93
Extensions to hierarchical margins......Page 96
Universality of n-fold integer programming......Page 98
Graver complexity of graphs and digraphs......Page 100
Nonlinear Combinatorial Optimization......Page 107
Preparation......Page 108
Matroids......Page 110
Matroid intersections......Page 113
Optimization over independence systems......Page 118
Approximative nonlinear optimization......Page 119
Exponential time to exact optimization......Page 127
Nonlinear bipartite matching......Page 129
Experimental design......Page 130
Universal Gröbner bases......Page 132
Bibliography......Page 139
Index......Page 145
