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On the Volumetric Path

Murat Mut (mhm309***at***lehigh.edu)
Tamás Terlaky (terlaky***at***lehigh.edu)

Abstract: We consider the logarithmic and the volumetric barrier functions used in interior point methods. In the case of the logarithmic barrier function, the analytic center of a level set is the point at which the central path intersects that level set. We prove that this also holds for the volumetric path. For the central path, it is also true that the analytic center of the optimal level set is the limit point of the central path. The only known case where this last property with the logarithmic barrier function fails occurs in case of semi definite optimization in the absence of strict complementarity. For the volumetric path, we show with an example that this property does not hold even for a linear optimization problem in canonical form.

Keywords: Logarithmic barrier function, volumetric barrier function, central path, volumetric path, interior point methods, analytic center, volumetric center

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Citation: Lehigh University Industrial & Systems Engineering Department, July 2010

Download: [Postscript]

Entry Submitted: 10/28/2010
Entry Accepted: 10/28/2010
Entry Last Modified: 10/28/2010

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