二阶锥约束随机变分不等式问题的数值方法研究

Numerical Method for Stochastic Variational Inequality Problems with Second-order Cone Constraints

本文研究二阶锥约束随机变分不等式(SOCCSVI)问题,运用样本均值近似(SAA)方法结合光滑Fischer-Burmeister互补函数来求解该问题.首先,将SOCCSVI问题的Karush-Kuhn-Tucker系统转化为与之等价的方程组,并证明了该方程组的雅可比矩阵的非奇异性.其次,构造了光滑牛顿算法求解该方程组.最后,文章给出了两个数值实验证明了算法的有效性.

In this paper,the second order cone-constrained stochastic variational inequality problem is studied.The sample average approximation(SAA)method combined with smooth Fischer-Burmeister function is used to solve this problem.First,the Karush-KuhnTucker system of the SOCCSVI problem is transformed into an equivalent equation system and after that,we prove the nonsingularity of the equation system’s Jacobian.Second,the smooth Newton algorithm is constructed to solve the equation system.Finally,there are two numerical experiments to prove the effectiveness of the algorithm.