Original scientific paper

Kernel-Based Interior-Point Methods for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones

Goran Lešaja ; Department of Mathematical Sciences, Georgia Suthern University, Statesboro, GA, United States of America

Abstract

We present an interior point method for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones (SCLCPs). The Cartesian P*(k)-SCLCPs have been recently introduced as the generalization of the more commonly known and more widely used monotone SCLCPs. The IPM is based on the barrier functions that are defined by a large class of univariate functions called eligible kernel function which have recently been successfully used to design new IPMs for various optimization problems. Eligible barrier (kernel) functions are used in calculating the Nesterov-Todd search directions and the default step-size which leads to a very good complexity results for the method. For some specific eligilbe kernel functions we match the best known iteration bound for the long-step methods while for the short-step methods the best iteration bound is matched for all cases.

Keywords

linear complementarity problem; Cartesian P*(k) property; Euclidean Jordan algebras and symmetric cones; interior-point method; kernel functions; polynomial complexity

Hrčak ID:

96609

URI

https://hrcak.srce.hr/96609

Publication date:

28.2.2011.

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