一致Cartesian-P二阶锥权互补问题的非单调下降算法

A Nonmonotone Descent Algorithm for the Uniform Cartesian-P Weighted Second-order Cone Complementarity Problem

运用下降算法求解二阶锥权互补问题.基于二阶锥权互补函数,构造一个价值函数,并在一致C artesian-P性质下证明该价值函数的强制性.运用该价值函数将二阶锥权互补问题转化为无约束最小化问题,提出求解二阶锥权互补问题的非单调下降算法.算法无需计算F(x)的雅可比矩阵,节省了迭代计算工作时间与内存.在单调性假设下,证明了算法全局收敛.最后数值实验表明算法是有效的.

In this paper,the descent algorithm is presented for solving the weighted secondorder cone complementarity problem.Based on the weighted second-order cone complementarity function,a merit function is constructed.The coerciveness of merit function is proved under the uniform Cartesian-P property.We reformulate the weighted second-order cone complementarity problem as an unconstrained minimization problem by the merit function,and propose a nonmonotone descent algorithm for solving the weighted second-order cone complementarity problem.This algorithm does not need to calculate the Jacobian matrix of F(x),which saves computation work and memory in each iteration.Under monotonicity assumption,the algorithm is shown globally convergent.Some numerical experiments show that the algorithm is effective.