Error bounds for mixed integer linear optimization problems

We introduce computable a priori and a posteriori error bounds for optimality and feasibility of a point generated as the rounding of an optimal point of the LP relaxation of a mixed integer linear optimization problem. Treating the mesh size of integer vectors as a parameter allows us to study the...

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Bibliographic Details
Published in:Mathematical programming Vol. 156; no. 1-2; pp. 101 - 123
Main Author: Stein, Oliver
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2016
Springer Nature B.V
Subjects:
Approximation
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Computer programming
Error analysis
Full Length Paper
Integers
Linear programming
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Mixed integer
Norms
Numerical Analysis
Optimization
Optimization techniques
Permissible error
Rounding
Studies
Theoretical
Vectors (mathematics)
United States > US
90C31
90C10
90C11
Hoffman constant
90C05
Rounding
Grid relaxation retract
Granularity
Global error bound
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:We introduce computable a priori and a posteriori error bounds for optimality and feasibility of a point generated as the rounding of an optimal point of the LP relaxation of a mixed integer linear optimization problem. Treating the mesh size of integer vectors as a parameter allows us to study the effect of different “granularities” in the discrete variables on the error bounds. Our analysis mainly bases on a global error bound for mixed integer linear problems constructed via a so-called grid relaxation retract. Relations to proximity results, the integer rounding property, and binary analytic problems are highlighted.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-015-0872-7