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

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 optimizationand 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.