We propose the algorithm that solves the symmetric cone programs (SCPs) by iteratively calling the projection and rescaling methods the algorithms for solving exceptional cases of SCP. Although our algorithm can solve SCPs by itself, we propose it intending to use it as a post-processing step for interior point methods since it can solve the problems more efficiently by using an approximate optimal (interior feasible) solution. We also conduct numerical experiments to see the numerical performance of the proposed algorithm when used as a post-processing step of the solvers implementing interior point methods, using several instances where the symmetric cone is given by a direct product of positive semidefinite cones. Numerical results show that our algorithm can obtain approximate optimal solutions more accurately than the solvers. When at least one of the primal and dual problems did not have an interior feasible solution, the performance of our algorithm was slightly reduced in terms of optimality. However, our algorithm stably returned more accurate solutions than the solvers when the primal and dual problems had interior feasible solutions.

翻译：我们提出了一种通过迭代调用投影与重缩放方法来解决对称锥规划（SCP）的算法，该算法专门用于处理SCP的异常情况。尽管所提算法本身能够独立求解SCP，但我们将其设计为内点法的后处理步骤，因为利用近似最优（内点可行）解能更高效地解决问题。我们还通过数值实验检验了该算法作为内点法求解器后处理步骤时的数值性能，实验采用了多个对称锥由正半定锥直积构成的实例。数值结果表明，与求解器相比，我们的算法能够更准确地获得近似最优解。当原问题与对偶问题中至少一方不存在内点可行解时，算法在最优性方面的性能略有下降；然而，当原问题与对偶问题均存在内点可行解时，本算法能够稳定地返回比求解器更精确的解。