Steepest Descent Method.md

![[Pasted image 20240524120326.png]] 最速下降法

Convergence of SDM

![[Pasted image 20240524123724.png]] 在目标函数是正定二次型函数时，SDM是R-线性收敛[[Algorithms for Unconstrained Optimization#R-convergence]]的

Kantorovich Inequality

![[Pasted image 20240524124541.png]]

Convergence analysis—quadratic form

SDM for L-Smooth and Convex Minimization

![[Pasted image 20240524124809.png]] ![[Pasted image 20240524124951.png]]

The Accelerated SDM for L-Smooth and Convex Minimization

![[Pasted image 20240524125105.png]] ![[Pasted image 20240524125121.png]]

Convergence of SDM—general form

![[Pasted image 20240524125143.png]] 在以上条件下， $\left{x^k\right}$ 的每一个聚点都是 $f$ 的stationary point[[Kuhn-Tucker Condition for Inequality-Constrained Optimization#The KKT Conditions]]

Remark

![[Pasted image 20240524125207.png]]

Application

![[Pasted image 20240618191742.png]]![[Pasted image 20240618191754.png]]