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.
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Wang, G., Zhu, D. A unified kernel function approach to primal-dual interior-point algorithms for convex quadratic SDO. Numer Algor 57, 537–558 (2011). https://doi.org/10.1007/s11075-010-9444-3
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DOI: https://doi.org/10.1007/s11075-010-9444-3
Keywords
- Convex quadratic semidefinite optimization
- Interior-point algorithm
- Kernel function
- Large- and small-update methods
- Iteration bound