求解非线性优化问题的Filter方法

序列二次规划是目前求解非线性规划约束问题的最有效的方法,但一般都采用罚函数法进行线性搜索,这使得它有很大的局限性,为了克服罚函数法存在的缺点,R.Fletcher和S.Leyff提出了一种filter方法取代了罚函数法,使迭代点能够保证目标函数或约束函数充分下降,理论分析和数值实验均表明,该方法优于传统的SQP算法。

Filter Method for the Solution of Nonlinear Optimization Problems

Sequential Quadratic Programming is the most efficient algorithm for nonlinear optimization.But it generally uses a penalty function to perform linear search,so it has prodigious limitation.A lot of work has been done to overcome the defaults of a penalty function.A filter method has been developed by the R Fltecher and S Leyffer,which avoids using a penalty parameter to weight the constraints and objective.It reduces either the objective function or the constraint violation function.Theoretical analysis and numerical experiments show that this kind of method is time-saving and has rapid convergence rate which surpassed the traditional SQP algorithm.