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An algorithmic framework for convex mixed integer nonlinear programs
A lift-and-project cutting plane algorithm for mixed 0–1 programs
We propose a cutting plane algorithm for mixed 0–1 programs based on a family of polyhedra which strengthen the usual LP relaxation. We show how to generate a facet of a polyhedron in this family…
Submodular set functions, matroids and the greedy algorithm: Tight worst-case bounds and some generalizations of the Rado-Edmonds theorem
The uncapacitated facility location problem
Abstract : An economic problem of great practical importance is to choose the location of facilities, such as industrial plants or warehouses, in order to minimize the cost (or maximize the profit)…
Combinatorial optimization : packing and covering
- G. Cornuéjols
Preface 1. Clutters 2. T-Cuts and T-Joins 3. Perfect Graphs and Matrices 4. Ideal Matrices 5. Odd Cycles in Graphs 6. 0,+1 Matrices and Integral Polyhedra 7. Signing 0,1 Matrices to Be Totally…
The traveling salesman problem on a graph and some related integer polyhedra
Some facet inducing inequalities of the convex hull of the solutions to the Graphical Traveling Salesman Problem are given and the so-called comb inequalities of Grötschel and Padberg are generalized.
A comparison of heuristics and relaxations for the capacitated plant location problem
Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms
The number of days required to clear a check drawn on a bank in city j depends on the city i in which the check is cashed. Thus, to maximize its available funds, a company that pays bills to numerous…
Recognizing Berge Graphs
This paper gives an algorithm to test if a graph G is Berge, with running time O(|V (G)|9), independent of the recent proof of the strong perfect graph conjecture.
Valid inequalities for mixed integer linear programs
- G. Cornuéjols
- MathematicsMath. Program.
- 19 July 2007
This tutorial introduces the necessary tools from polyhedral theory and gives a geometric understanding of several classical families of valid inequalities such as lift-and-project cuts, Gomory mixed integer cuts, mixed integer rounding cuts, split cuts and intersection cuts, and it reveals the relationships between these families.