优化问题的序列线性方程组解法

拟牛顿算法是求解无约束优化问题的有效算法.序列二次规划方法是将拟牛顿算法应用于求解约束优化的推广与发展,它保持了拟牛顿算法的超线性收敛速度而成为约束优化的重要算法类.序列线性方程组方法则是它的进一步发展,目的在于每步求迭代方向dk时避免求解计算量较大的二次子规划.现在序列线性方程组方法仍在研究和发展,目的是简化算法结构、减少计算量,同时保持算法的优良性质.

Algorithm of Sequential Systems of Linear Equations for Optimization Problems

In this paper,we introduce some algorithms of sequnential systems of linear equations (SSLE) for nonlinear optimization problems.Sequential quadratic programming (SQP) algorithms have good properties of global convergence and superlinear convergence rate.But solving a quadratic programming is to be required consuming a large amount of computation in every step of SQP algorithm for getting the iterative direction d_k. All SSLE type algorithm are to be developed form SQP algorithm.Now,Our aim of continuing study SSLE algorithm is to simplify the structure of the algorithm and only need solving a systems of linear equations for getting d_k.