中科大-凸优化 笔记（lec47）-最速下降法
本文共 520 字，大约阅读时间需要 1 分钟。
全部笔记的汇总贴（视频也有传送门）：
一、梯度下降法
d k + 1 = − ∇ f ( x k ) f ( x k + 1 ) − P ∗ f ( x k ) − P ∗ ≤ 1 − m M ≤ 1 − min { 2 m γ α m a x , 2 m γ β M } K ∼ log ( f ( x k ) − P ∗ ) 线 性 收 敛 d^{k+1}=-\nabla f(x^k)\\\frac{f(x^{k+1})-P^*}{f(x^k)-P^*}\le1-\frac mM\le1-\min\{2m\gamma\alpha_{max},\frac{2m\gamma\beta}M\}\\ K\sim \log(f(x^k)-P^*)\;\;\;\;\;线性收敛 dk+1=−∇f(xk)f(xk)−P∗f(xk+1)−P∗≤1−Mm≤1−min{ 2mγαmax,M2mγβ}K∼log(f(xk)−P∗)线性收敛
二、最速（陡）下降法
三、Gradient与Steepest Gradient的变种
1）坐标轮换法
2）若 f ( x ) f(x) f(x)在某些点不可微
例：
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