二阶锥线性互补问题的两种新光滑型算法

Two Novel Smooth-type Algorithms for Second-Order Cone Linear Complementarity Problems

本文研究二阶锥线性互补问题的两种低阶罚函数光滑型算法.利用核函数卷积积分为正函数和负函数生成光滑函数的方法,提出了两种新的光滑函数,并利用光滑牛顿法进行数值实验,获得了当罚参数趋于无穷大、光滑参数单调下降趋于零时,低阶罚函数方程组解序列在特定条件下收敛于二阶锥线性互补问题解的结果.通过数值实验将新提出的光滑函数与原有的光滑函数进行性能比较,结果表明新光滑函数之一具有更好的数值性能,这推广了投影函数的光滑函数.

This paper presents two novel smooth-type functions of lower order penalty function algo-rithms for solving the second-order cone linear complementarity problem.These two new smooth functions are introduced by employing the method of generating smooth functions whose convolutional integration of kernel functions is the plus function and minus function.Numerical experiments are subsequently con-ducted using the smooth Newton method.The results demonstrate that as the penalty parameter tends to in nity and the smooth parameter monotonically decreases to zero,the solution sequence of the lower or-der penalty equations converges to the solution of the second-order cone linear complementarity problems under certain assumption.Furthermore,a comparison of the performance between the newly proposed smooth functions and the original smooth functions is carried out through numerical experiments.The ndings indicate that one of the new smooth functions exhibits better numerical performance.Thereby,this generalizes the smooth functions of the projection function.