Index
approximation algorithms, 85
Barrier Algorithm, 121
Berge graph, 44
blocker, 51
Branch-and-bound, 1
Brion and Vergne's formula, 71
CaTs, 103
chromatic number, 43
Chvatal-Gomory (CG) inequality, 22
clutter, 39
contingency table, 110
convex programming, 119
cover inequality, 27
CPLEX, 24
cutting planes, 1
determinant of the lattice, 6
Dickson's Lemma, 101
disclosure limitation, 110
disjunctive formulations, 26
dual ascent method, 91
4ti2, 102
facility location, 85
Farkas lemma, 78
First-order optimality conditions, 117
fractional cuts, 23
global solution to, 116
Gomory relaxation, 76
Grobner basis, 100, 101
Grobner cone, 103
Grobner fan, 103
Graver basis, 100, 104
H. W. Lenstra, Jr., 2
Herbert Scarf, 102
Hessian of the Lagrangian, 128
hierarchical model, 110
Hilbert basis, 100, 103
Hilbert series, 100
Homogeneous Pair, 46
integer programming gap, 103, 106
integer width, 5
Interior-Point Methods, 126
IPOPT, 128
/c-median problem, 96
Konig, 40
knapsack problem, 27
KNITRO, 128
Lagrangian multiplier, 96
Lagrangian, 118
Laplace transform, 69
LattE, 109
lattice, 6
lattice basis, 6
lattice basis reduction, 2
lattice point free, 5
Legendre-Fenchel transform, 69
Lehman's Characterization, 57
Lenstra's algorithm, 5
lifting, 25
lifting problem, 25
LINDO, 24
linear programming relaxation, 87
LOQO, 128
matching, 39
Max Flow Min Cut property, 41
Menger, 40
method of multipliers, 124
Minkowski, 4
mixed-integer program, 21
neighbors of the origin, 102
Newton's Method, 120
Nonlinear programming, 115
odd hole, 44
optimal value, 99
optimality conditions, 117
orthogonality defect, 11
packing property, 41
Perfect Graph Theorem, 45
139
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