New complexity analysis for primal-dual interior-point methods for self-scaled optimization problems

作者：Choi Bo Kyung; Lee Gue Myung^*

来源：Fixed Point Theory and Applications, 2012, 213.

DOI：10.1186/1687-1812-2012-213

• Euclidean Jordan algebra
• self-scaled optimization problem
• primal-dual interior-point methods
• kernel function
• proximity function
• complexity analysis
• worst-case iteration bound

A linear optimization problem over a symmetric cone, defined in a Euclidean Jordan algebra and called a self-scaled optimization problem (SOP), is considered. We formulate an algorithm for a large-update primal-dual interior-point method (IPM) for the SOP by using a proximity function defined by a new kernel function, and we obtain the best known complexity results of the large-update IPM for the SOP by using the Euclidean Jordan algebra techniques.

• 出版日期2012