A new non-interior point algorithm for circular cone programming

Abstract:

A new non-interior point algorithm is proposed for solving the circular cone programming (CCP). Based on the relationship between the circular cone and the second-order cone, a projection equation that is equivalent to the complementary condition of the CCP is introduced.Then the problem is transformed into a linear system of equations. The method only needs to solve the linear equations with the same coefficient matrix and compute two projections at each iteration. Moreover, the algorithm can start from an arbitrary point and does not require the row vectors of the affine constraint coefficient matrix to be linearly independent. Under weaker assumptions, the global convergence of the algorithm is proved. Numerical results show that the algorithm is fast and effective.