A smoothing Newton algorithm based on a one-parametric class of smoothing functions for linear programming over symmetric cones

A smoothing Newton algorithm based on a one-parametric class of smoothing functions for linear programming over symmetric cones

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Article ID: iaor200971931
Country: Germany
Volume: 70
Issue: 2
Start Page Number: 385
End Page Number: 404
Publication Date: Oct 2009
Journal: Mathematical Methods of Operations Research
Authors: ,
Keywords: cone decomposition
Abstract:

In this paper, we introduce a one-parametric class of smoothing functions which contains the Fischer–Burmeister smoothing function and the Chen-Harker-Kanzow-Smale (CHKS) smoothing function as special cases. Based on this class of smoothing functions, a smoothing Newton algorithm is extended to solve linear programming over symmetric cones. The global and local quadratic convergence results of the algorithm are established under suitable assumptions. The theory of Euclidean Jordan algebras is a basic tool in our analysis.

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