Solving second order cone programming via a reduced augmented system approach. (English) Zbl 1128.90045
Summary: The standard Schur complement equation-based implementation of interior-point methods for second order cone programming may encounter stability problems in the computation of search directions, and as a consequence, accurate approximate optimal solutions are sometimes not attainable. Based on the eigenvalue decomposition of the \((1,1)\) block of the augmented equation, a reduced augmented equation approach is proposed to ameliorate the stability problems. Numerical experiments show that the new approach can achieve more accurate approximate optimal solutions than the Schur complement equation-based approach.
MSC:
90C20 | Quadratic programming |
90C22 | Semidefinite programming |
90C51 | Interior-point methods |
65K05 | Numerical mathematical programming methods |