解变分不等式问题的一类滤子SQP算法

Filter SQP algorithm for variational inequality problem

针对一般形式的变分不等式问题,考虑将其转化为约束优化问题求解.对于这种特定的约束优化问题,提出了一类新的滤子序列二次规划(SQP)求解方法.基于变分不等式与约束优化问题的不同,在滤子条件中采用了一个二次价值函数作为目标函数,使得一般的变分不等式问题均可用滤子算法求解.采用SQP方法结合滤子方法获取试探步,只需要计算两个简单不等式判断试探步,算法易实现,计算量小.在较弱的条件下证明了算法的全局收敛性.最后,给出了算法的数值算例,与同类算法比较,结果良好.

The variational inequality problem was reformulated as equivalent constrained optimization problem.A new filter SQP method was proposed to solve the constrained optimization problem.Based on the difference between variational inequality problem and constrained optimization problem,a quadratic merit function was adopted at filter conditions to solve the general variational inequality problem by the filter algorithm.A trial step was obtained by SQP method combined with filter technique.Only two inequalities were needed to determine the trial step with less computation work.Under mild conditions,the global convergence was established to provide some numerical examples.The numerical results show good efficiency of the proposed method.