Multiple Cuts with a Homogeneous Analytic Center Cutting Plane Method

Olivier Péton (petonhec.unige.ch)
Jean-Philippe Vial (vialhec.unige.ch)

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 cut 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(plog 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 $\sqrt p$.

Keywords: Cutting planes, analytic center, conic formulation, multiple cuts

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: HEC/Logilab Technical Report 2001.1 40, bd du Pont d'Arve CH-1211 Geneva 4, Switzerland

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Entry Submitted: 05/25/2001
Entry Accepted: 05/30/2001
Entry Last Modified: 05/25/2001

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