A unified kernel function approach to interior-point methods for the Cartesian P(K)-LCP over symmetr

来源 :Shanghai Workshop on Numerical Algebra,Imaging and Optimizat | 被引量 : 0次 | 上传用户:sz_ocean
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Kernel functions play an important role in the design and analysis of interior-point methods(IPMs).They are not only used for determining the search directions but also for measuring the distance between the given iterate and the μ-center for the algorithms.In this talk,we give a unified computational scheme for the complexity analysis of kernel function based IPMs for the Cartesian P*(K)-linear complementarity problem over symmetric cones.By using Euclidean Jordan algebras,the currently best known iteration bounds for large-and small-update methods are derived,namely,O{(1+2k)√rlogrlogr/ε}and O(1+2k)√rlogr/ε},respectively.Furthermore,this unifies the analysis for the P*(k)-LCP,the Cartesian P*(k)-second-order cone linear complementarity problem,and the Cartesian P*(k)-semidefinite linear complementarity problem.
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