带误差的等式约束优化问题的BFGS-SQP-L方法分析

Analysis of BFGS-SQP-L method in equality constrained optimization with errors

针对一类等式约束下目标函数及其梯度存在一定误差的优化问题,将经典的BFGS公式嵌入误差下的序列二次规划(SQP)框架,采用拉格朗日线搜索(L)步长,给出了该问题的BFGS-SQP-L迭代算法。所采用的延长差分技术,可保证算法的可行性。进一步,如果目标函数及其梯度估值的误差是一致有界的,那么迭代收敛到解的邻域,且解的大小取决于误差。

For a class of equality constrained optimization problems with certain errors in corresponding objective functions and their gradients,we propose a BFGS-SQP-L algorithm to solve these problems by embedding the classical BFGS formula into the framework of SQP with errors with steps of outline of Lagrange.The extended difference technique here can ensure the feasibility of the algorithm,and if both the error of the underlying objective function and the error of its gradient estimation are uniformly bounded,then the algorithm iteration converges to the neighborhood of the true solution with the size of the convergence solution depending on the error.