ACCPM with a nonlinear constraint and an active set strategy to solve nonlinear multicommodity flow problems |
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Authors: | F Babonneau J-P Vial |
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Institution: | (1) Logilab, HEC, Université de Genève, 40 Bd du Pont d’Arve, 1211 Geneva, Switzerland |
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Abstract: | This paper proposes an implementation of a constrained analytic center cutting plane method to solve nonlinear multicommodity
flow problems. The new approach exploits the property that the objective of the Lagrangian dual problem has a smooth component
with second order derivatives readily available in closed form. The cutting planes issued from the nonsmooth component and
the epigraph set of the smooth component form a localization set that is endowed with a self-concordant augmented barrier.
Our implementation uses an approximate analytic center associated with that barrier to query the oracle of the nonsmooth component.
The paper also proposes an approximation scheme for the original objective. An active set strategy can be applied to the transformed
problem: it reduces the dimension of the dual space and accelerates computations. The new approach solves huge instances with
high accuracy. The method is compared to alternative approaches proposed in the literature.
An erratum to this article can be found at |
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Keywords: | Constrained ACCPM Approximation scheme Active set strategy |
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