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Error bounds for mixed integer linear optimization problems

Oliver Stein (stein***at***kit.edu)

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 the construction of a so-called grid relaxation retract. Relations to proximity results and the integer rounding property are highlighted.

Keywords: Error bound, grid relaxation retract, granularity, Hoffman constant

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Citation: Mathematical Programming, Vol. 156 (2016), 101-123, DOI 10.1007/s10107-015-0872-7.

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Entry Submitted: 11/25/2013
Entry Accepted: 11/25/2013
Entry Last Modified: 02/15/2016

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