Journal
NUMERICAL ALGORITHMS
Volume 57, Issue 4, Pages 537-558Publisher
SPRINGER
DOI: 10.1007/s11075-010-9444-3
Keywords
Convex quadratic semidefinite optimization; Interior-point algorithm; Kernel function; Large-and small-update methods; Iteration bound
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Funding
- National Natural Science Foundation of China [11001169, 10871130]
- China Postdoctoral Science Foundation [20100480604]
- Ph.D. Foundation [20093127110005]
- Shanghai Leading Academic Discipline Project [T0401]
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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 mu-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.
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