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

作者：Wang, Guoqiang^*; Zhu, Detong

来源：Numerical Algorithms, 2011, 57(4): 537-558.

DOI：10.1007/s11075-010-9444-3

• Convex quadratic semidefinite optimization
• Interior-point algorithm
• Kernel function
• Large-and small-update methods
• Iteration bound

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.

• 出版日期2011-8
• 单位上海师范大学; 上海工程技术大学