二阶锥规划的光滑非精确牛顿法

Smoothing Inexact Newton Method for the Second Order Cone Programming

摘要: 本文给出了一个新的求解二阶锥规划的光滑非精确牛顿法。在每次迭代时，新方法采用非精确牛顿法去求解一个方程组的解，降低了光滑牛顿法的计算量。在较弱条件下，证明了算法具有全局和局部二阶收敛性质。数值试验表明算法是有效的。

Abstract: A new smoothing inexact Newton method is presented for solving the second-order cone pro-gramming. At each iteration, the method uses an inexact Newton method to solve the system of equations, which saves computation work of smoothing Newton methods. Under weak assumptions, our method is proved to have global and local quadratic convergence. Numerical experiments indicate that the proposed method is quite effective.