求解圆锥规划的光滑牛顿法

A Smoothing Newton Algorithm for Circular Cone Programming

圆锥规划是一类重要的非对称锥优化问题.基于一个光滑函数,将圆锥规划的最优性条件转化成一个非线性方程组,然后给出求解圆锥规划的光滑牛顿法.该算法只需求解一个线性方程组和进行一次线搜索.运用欧几里得约当代数理论,证明该算法具有全局和局部二阶收敛性.最后数值结果表明算法的有效性.

In this paper, we consider the circular cone programming, which is a kind of important nonsymmetric cone optimization problem. Based on a smoothing function, we re- formulate the optimality conditions of the circular cone programming as a system of nonlinear equations, and propose a smoothing Newton method for solving circular cone programming problem. The algorithm solves only one linear system of equations approximately and performs only one line search at each iteration. The proposed algorithm is shown to be globally and locally quadratically convergent by using the Euclidean Jordan algebra theory. Finally, numerical results illustrate the effectiveness of our new algorithm.