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

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。

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.