二阶锥规划的光滑牛顿算法

A Smoothing Newton Method for Second-order Cone Programming

基于光滑Fischer-Burmeister函数,给出一个求解二阶锥规划的光滑牛顿算法。算法对于初始点的选取没有任何限制,并且在每一步迭代时只需要求解一个线性方程组,只进行一次线搜索。同时在不满足严格互补的条件下,证明了算法是全局收敛的和局部二次收敛的。数值试验结果表明算法的有效性。

Based on the Fischer-Burmeister smoothing function, a smoothing Newton method is presented for solving the second-order cone programming. The proposed algorithm does not have re- strictions regarding its starting point, and solves only one linear system of equations and performs only one line search at each iteration. Without requiring strict complementarity assumption, the proposed al- gorithm is proved to be globally and locally quadratically convergent under suitable assumptions. Nu- merical results indicate that the algorithm is efficient in practical comnutation.