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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Vydáno v:	Mathematical programming Ročník 156; číslo 1-2; s. 101 - 123
Hlavní autor:	Stein, Oliver
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2016 Springer Nature B.V
Témata:	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
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Abstract	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.
AbstractList	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.
Author	Stein, Oliver
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Cites_doi	10.1137/0313015 10.1007/s10107-011-0481-z 10.1137/S0895479892237744 10.1137/S1052623402403505 10.1016/0024-3795(93)90125-8 10.1137/0804021 10.1137/S1052623495284832 10.1007/BF01582230 10.1007/s10107-012-0518-y 10.1007/978-3-642-97881-4 10.1137/S036301299222723X 10.1007/BF01432655 10.1007/BF01582210 10.1007/BF01580862 10.6028/jres.049.027 10.1287/moor.13.2.243 10.1287/moor.10.2.175 10.1016/0024-3795(92)90174-9 10.1137/0325033 10.1007/978-3-540-68279-0 10.1137/0602044 10.1007/s10107-014-0806-9
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SubjectTerms	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)
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Title	Error bounds for mixed integer linear optimization problems
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