一种修正的线搜索Filter-SQP算法

A MODIFIED LINE SEARCH FILTER-SQP ALGORITHM

序列二次规划(SQP)算法是解非线性优化问题最有效的方法之一,然而当QP子问题不相容时SQP算法将会失败,且在罚函数中选择合适的罚参数比较困难.此处在原Filter-SQP算法的基础上,利用特定的凸规划模型代替QP子问题,提出一种修正的线搜索filter-SQP算法,并证明它的全局收敛性.此算法原理简单,容易实现,且具有全局收敛性,数值实验表明它是有效的.

The sequential quadratic programming （SQP） algorithm is one of the most effective methods of solving nonlinear optimization problems, however when its quadratic programming （QP） sub-problem is not consistent, the SQP algorithm will fail to obtain the search direction, and it is also difficult to determine a suitable value of the penalty parameter in the merit function. Based on the original Filter- SQP algorithm, in this paper the author proposes a modified line search Filter-SQP algorithm and proves its global convergence, where the QP sub-problem is replaced by the special convex programming. The modified algorithm is simple, implemented easily and of global convergence under some condition, and the numerical tests show the efficiency of this modified method.