In this paper, we propose a line search penalty-free method for solving nonlinear second-order cone programming (NSOCP) problem. Compared with the traditional SQP-type method for NSOCP, our method does not need the assumption that the subproblem is feasible. Besides that, it does not use penalty-function or filter technique. We first use a robust linear second-order cone programming subproblem to get a detective step and then compute an optimal step from a quadratic optimization subproblem. The search direction is a convex combination of the detective step and optimal step. This two-phase strategy and the penalty-free technique are employed to promote global convergence which is analyzed under mild assumptions. We report some numerical experiments whose results show that the proposed algorithm is applicable and efficient.

在本文中，我们提出了一种用于解决非线性二阶锥规划（NSOCP）问题的线搜索无罚方法。与用于NSOCP的传统SQP型方法相比，我们的方法不需要假设子问题是可行的。除此之外，它不使用惩罚函数或滤波技术。我们首先使用一个鲁棒的线性二阶锥规划子问题来得到一个检测步骤，然后根据二次优化子问题来计算一个最优步骤。搜索方向是检测步骤和最佳步骤的凸组合。该两阶段策略和无罚技术被用来促进全局收敛，这是在温和的假设下进行分析的。我们报告了一些数值实验，其结果表明该算法是适用和有效的。