Kantorovich不等式的推广及其在最速下降法 分析中的应用

An Extension of Kantorovich Inequality with an Application in the Analysis of Steepest Decent Method

摘要: 本文利用最优化理论中经典的Kuhn-Tucker条件证明并推广了Kantorovich不等式。作为应用，将极小化正定二次函数的最速下降法的收敛速度分析推广到半正定情形。
>Based on Kuhn-Tucker condition in optimization theory, we extend the canonical Kantorovich inequality. As an application, the analysis on the convergence rate of steepest descent for minimizing a posi-tive definite quadratic function is extended for the positive semi-definite case.