A unified kernel function approach to primal-dual interior-point algorithms for convex quadratic SDO

Authors:
Guoqiang Wang;Detong Zhu
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai, People's Republic of China 200234 and College of Advanced Vocational Technology, Shanghai University of Engineering Science, Shangh ...;Department of Mathematics, Shanghai Normal University, Shanghai, People's Republic of China 200234
Venue:
Numerical Algorithms
Year:
2011

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Abstract

Kernel functions play an important role in the design and analysis of primal-dual interior-point algorithms. 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 paper we present a unified kernel function approach to primal-dual interior-point algorithms for convex quadratic semidefinite optimization based on the Nesterov and Todd symmetrization scheme. The iteration bounds for large- and small-update methods obtained are analogous to the linear optimization case. Moreover, this unifies the analysis for linear, convex quadratic and semidefinite optimizations.