A deep cut ellipsoid algorithm for convex programming: Theory and applications

A deep cut ellipsoid algorithm for convex programming: Theory and applications

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Article ID: iaor19951853
Country: Netherlands
Volume: 63
Issue: 1
Start Page Number: 83
End Page Number: 108
Publication Date: Jan 1994
Journal: Mathematical Programming (Series A)
Authors: , ,
Abstract:

This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min-max stochastic queue location problem are reported.

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