一种求解序列二次规划结合信赖域的多维滤子算法

求解非线性规划问题最有效的方法之一为序列二次规划。但是,由于序列二次规划结合信赖域时,会出现可能无解的情况(即不相容性)。而本文针对不相容性提出了一类序列二次规划结合信赖域的多维相容滤子算法。首先,本文根据一般文献中提及的方法对其约束条件引进参数变量,对其目标函数加以惩罚,即实行了可行化处理(也就是无需可行性恢复阶段),从而克服了不相容性。其次,本文提出了多维滤子条件来对迭代步进行选择性的接受,从而避免了传统二维滤子算法的严格条件,使得对迭代步的接受程度大大的放松。最后针对可能出现的maratos效应,我们通过二阶校正策略提出了一种修改后的多维滤子算法。同时,在一定的假设条件下算法具有全局收敛性。

A Multidimensional Filter Algorithm for Sequential Quadratic Programming with Trust Region

Sequential quadratic programming(SQP)is one of the most effective methods for solving nonlinear programming(NLP)problems. However, due to the combination of trust region and SQP, there may be no solution(i.e. incompatibility). In view of incompatibility, a multidimensional compatible filter algorithm based on SQP and trust region is proposed. Firstly, according to the methods mentioned in the general literature, this paper introduces parameter variables to its constraints and punishes its objective function, which implements the feasibility treatment to overcome the incompatibility(i.e. without feasibility recovery stage). Secondly, this paper proposes a multi-dimensional filter condition to selectively accept the iteration step, thus avoiding the strict conditions of the traditional two-dimensional filter algorithm, which greatly relaxes the acceptance of the iteration step. Finally, we propose a modified multi-dimensional filter algorithm based on second-order correction strategy for possible effects. At the same time, the algorithm has global convergence under certain assumptions.