Extended formulations for convex envelopes
Martin Ballerstein (martin.ballerstein@ifor.math.ethz.ch) and
Dennis Michaels (dennis.michaels@math.tu-dortmund.de)
Journal of Global Optimization, 2014, vol. 60, issue 2, 217-238
Abstract:
In this work we derive explicit descriptions for the convex envelope of nonlinear functions that are component-wise concave on a subset of the variables and convex on the other variables. These functions account for more than 30 % of all nonlinearities in common benchmark libraries. To overcome the combinatorial difficulties in deriving the convex envelope description given by the component-wise concave part of the functions, we consider an extended formulation of the convex envelope based on the Reformulation–Linearization-Technique introduced by Sherali and Adams (SIAM J Discret Math 3(3):411–430, 1990 ). Computational results are reported showing that the extended formulation strategy is a useful tool in global optimization. Copyright Springer Science+Business Media New York 2014
Keywords: Convex envelope; Edge-concave functions; Extended formulation; Reformulation–Linearization-Technique; Simultaneous convexification (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:jglopt:v:60:y:2014:i:2:p:217-238
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DOI: 10.1007/s10898-013-0104-8
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