二阶锥规划基于SOC函数的新光滑牛顿算法
A New Smoothing Newton Method for Se-cond-Order Cone Optimization Based on SOC Function
DOI: 10.12677/AAM.2019.84067, PDF,    国家自然科学基金支持
作者: 梁晓娟, 曾友芳：广西大学数学与信息科学学院，广西 南宁
关键词: 二阶锥规划；光滑牛顿法；全局收敛；局部二次收敛；Second-Order Cone Programming； Smoothing Newton Method； Global Convergence； Quadratical Convergence
摘要: 本文在向量值Fischer-Burmeister (FB)函数和向量值Natural-Residual (NR)函数的基础上，提出一种求解二阶锥规划(SOCP)问题的光滑函数。用一个带扰动的牛顿方程组去获得搜索方向，在适当假设下，分析了算法的全局收敛和局部收敛速度，给出了数值实验结果。
Abstract: Based on the Fischer-Burmeister function and the Natural-Residual function, a new smoothing Newton method is proposed for solving the second-order cone programming. This algorithm adopts a Newton equation with disturbance to gain the search direction. Under suitable assumptions, we prove that the proposed method is globally and locally quadratically convergent. Finally, some numerical results are given.
文章引用：梁晓娟, 曾友芳. 二阶锥规划基于SOC函数的新光滑牛顿算法[J]. 应用数学进展, 2019, 8(4): 602-612. https://doi.org/10.12677/AAM.2019.84067

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