The LP-Newton method solves linear programming (LP) problems by repeatedly projecting a current point onto a certain relevant polytope. In this paper, we extend the algorithmic framework of the LP-Newton method to conic programming (CP) problems via a linear semi-infinite programming (LSIP) reformulation. In this extension, we produce a sequence by projection onto polyhedral cones constructed from LP problems obtained by finitely relaxing the LSIP problem equivalent to the CP problem. We show global convergence of the proposed algorithm under mild assumptions. To investigate its efficiency, we apply our proposed algorithm and a primal-dual interior-point method to second-order cone programming problems and compare the obtained results.

LP-牛顿法通过将当前点重复投影到某个相关的多面体上来解决线性规划（LP）问题。在本文中，我们通过线性半无限规划（LSIP）重构将LP-牛顿法的算法框架扩展到圆锥规划（CP）问题。在此扩展中，我们通过投影到由有限问题通过等效于CP问题的LSIP问题而获得的LP问题构造的多面锥上产生序列。我们展示了在温和假设下所提出算法的全局收敛性。为了研究其效率，我们将我们提出的算法和原始对偶内点方法应用于二阶锥规划问题，并比较所获得的结果。