等方向线的概念及其在无约束最优化中的应用前景

The Line with Same Direction of Gradient and Its Application in Unconstrained Optimization

本文首次提出了等方向线的概念、讨论了其特征及其在无约束最优化中的应用前景:探讨了构筑无矩阵且具二阶收敛的算法和开辟新的全局最优化研究领域的可能性。 本文还讨论了等方向线在全局最优化和非线性方程组求解中的应用前景。

A new concept, the Line with Same Direction of Gradient, and its characteristic were first given. The possibility to construct unconstraint optimization methods whose convergence is quadratic without matrix was discussed. It is possible to use the concept to global optimization, nonlinear equation problems and other mathematical or physical problems.