Optimization Letters

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

Error bounds for mixed integer nonlinear optimization problems

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  


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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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