无约束优化问题的对角二阶拟柯西法

A Diagonal Second-order Quasi-Cauchy Method for Unconstrained Optimization Problem

通过引入最小改变的对角修正策略,结合弱二阶拟牛顿方程,设计一种新的求解无约束优化问题的对角二阶拟柯西法,此算法保证了修正矩阵的非奇异性.在适当的假设条件下,进一步分析算法的线性收敛性.数值试验结果表明,该算法是有效且可行的.

Based on the second-order quasi-Newton equation and least-change diagonal updating strategy,we propose a diagonal second-order Quasi-Cauchy method,which guarantees the non-singularity of the updating formula. In the appropriate assumptions, we prove the linear convergence of the algorithm to go a step further. Numerical results also show that the new algorithm is more stable and more effective.