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A smoothing Newton algorithm based on a one-parametric class of smoothing functions for linear programming over symmetric cones. (English) Zbl 1175.90290
Summary: We introduce a one-parametric class of smoothing functions which contains the Fischer-Burmeister smoothing function and the 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.

90C05 Linear programming
90C22 Semidefinite programming
90C25 Convex programming
90C30 Nonlinear programming
Full Text: DOI
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