# American Institute of Mathematical Sciences

2015, 5(2): 211-231. doi: 10.3934/naco.2015.5.211

## Primal-dual interior-point algorithms for convex quadratic circular cone optimization

 1 Department of Mathematics, Shanghai University, Shanghai 200444, China, China 2 College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620

Received  December 2014 Revised  May 2015 Published  June 2015

In this paper we focus on a class of special nonsymmetric cone optimization problem called circular cone optimization problem, which has a convex quadratic function as the objective function and an intersection of a non-self-dual circular cone and linear equations as the constraint condition. Firstly we establish the algebraic relationships between the circular cone and the second-order cone and translate the original problem from the circular cone optimization problem to the second-order cone optimization problem. Then we present kernel-function based primal-dual interior-point algorithms for solving this special circular cone optimization and derive the iteration bounds for large- and small-update methods. Finally, some preliminary numerical results are provided to demonstrate the computational performance of the proposed algorithms.
Citation: Yanqin Bai, Xuerui Gao, Guoqiang Wang. Primal-dual interior-point algorithms for convex quadratic circular cone optimization. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 211-231. doi: 10.3934/naco.2015.5.211
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##### References:
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