Multiple Cuts with a Homogeneous Analytic Center Cutting Plane Method

Abstract : This paper analyzes the introduction of multiple central cuts in a conic formulation of the analytic center cutting plane method (in short ACCPM). This work extends earlier work on the homogeneous ACCPM, and parallels the analysis of the multiple cuts process in the standard ACCPM. The main issue is the calculation of a direction that restores feasibility after introducing p new cutting planes at the query point. We prove that the new analytic center can be recovered in O (p log wp) damped Newton iterations, where w is a parameter depending of the data. We also present two special cases where the complexity can be decreased to O (p log p). Finally, we show that the number of calls to the oracle is the same as in the single cut case, up to a factor
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https://hal.archives-ouvertes.fr/hal-01232556
Contributor : Olivier Péton <>
Submitted on : Monday, November 23, 2015 - 4:37:31 PM
Last modification on : Tuesday, December 4, 2018 - 10:42:03 AM

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Olivier Péton, Jean-Philippe Vial. Multiple Cuts with a Homogeneous Analytic Center Cutting Plane Method. Computational Optimization and Applications, Springer Verlag, 2003, 2 (1), pp.37-61. ⟨http://link.springer.com/article/10.1023%2FA%3A1021845931805#⟩. ⟨10.1023/A:1021845931805⟩. ⟨hal-01232556⟩

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