二阶锥规划一个超线性收敛的非内部连续化算法

基于非光滑向量值最小函数的一个新光滑函数, 建立了二阶锥规划一个超线性收敛的非内部连续化算法. 该算法的特点如下: 首先, 初始点任意; 其次, 每次迭代只需求解一个线性方程组即可得到搜索方向; 最后, 在无严格互补假设下, 获得算法的全局收敛性、强收敛性和超线性收敛性. 数值结果表明算法是有效的.

A non-interior-point continuous algorithm with superlinear convergence for second-order cone programming

In this paper, based on a new smoothing function of the well-known nonsmooth vector-valued min-function, a non-interior-point continuous algorithm for second-order cone programming is presented. The features of this method are as follows: firstly, the starting point can be chosen arbitrarily; secondly, at each iteration, only one system of linear equations is performed for searching an improving direction; finally, global, strong and superlinear convergence are obtained without assumption of strict complementarity. The numerical results demonstrate the effectiveness of the algorithm.