Optimization Letters

, Volume 10, Issue 6, pp 1153–1168 | Cite as

Error bounds for mixed integer nonlinear optimization problems

  • Oliver Stein
Original Paper


We introduce a-posteriori and a-priori error bounds for optimality and feasibility of a point generated as the rounding of an optimal point of the NLP relaxation of a mixed-integer nonlinear optimization problem. Our analysis mainly bases on the construction of a tractable approximation of the so-called grid relaxation retract. Under appropriate Lipschitz assumptions on the defining functions, we thereby generalize and slightly improve results for the mixed-integer linear case from Stein (Mathematical Programming, 2015, doi: 10.1007/s10107-015-0872-7). In particular, we identify cases in which the optimality and feasibility errors tend to zero at an at least linear rate for increasingly refined meshes.


Rounding Granularity Grid relaxation retract  Global error bound  



The author is grateful to the anonymous referee and the associate editor for their precise and substantial remarks on an earlier version of this manuscript.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of Operations ResearchKarlsruhe Institute of Technology (KIT)KarlsruheGermany

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