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The proximal Chebychev center cutting plane algorithm for convex additive functions

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Abstract

The recent algorithm proposed by the author for convex nonsmooth optimization is tailored to the case where the objective function is additive. We highlight aspects where this specialization differs from ignoring the structure of the objective function. To assess the approach, we consider two different nonlinear multicommodity flows applications in telecommunications including some comparison with a proximal bundle algorithm.

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Notes

  1. The implementation of bfull is exactly the same as in [27] except that we use here a different version of CPLEX which results in slight differences in term of oracle calls.

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Acknowledgments

I’m indebted to the reviewers and the associate editors for their comments and suggestions which greatly improve an earlier version of this paper. I’m grateful to Antonio Frangioni for interesting and useful discussions on aggregation strategies.

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Correspondence to Adam Ouorou.

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Dedicated to Claude Lemaréchal on the occasion of his 65th birthday.

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Ouorou, A. The proximal Chebychev center cutting plane algorithm for convex additive functions. Math. Program. 140, 163–187 (2013). https://doi.org/10.1007/s10107-012-0630-z

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