Gradient Lipschitz continuous：Gradient Descent
Gradient Descent
I.e.,∇fisLipschitzcontinuouswithconstantL>0.Theorem:Gradientdescentwithfixedstepsizet≤1/Lsatisfiesf(x(k))−f?≤kx(0)−x?k2.2.2tk.。其他文章還包含有：「1.Gradientmethod」、「Lipschitzcontinuousgradient·XingyuZhou'sblog」、「Chapter3Gradient」、「Lipschitzcontinuity」、「IsaLipschitzcontinuousgradientequivalenttothis...」、「Lipschitzcontinuousgradientandquadraticboundproperty」、「NotesonConve...
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1. Gradient method
https://www.seas.ucla.edu
• analysis of gradient method. Page 12. Lipschitz continuous gradient the gradient of ???? is Lipschitz continuous with parameter ???? > 0 if k∇ ???? (????)−∇ ???? ...
Lipschitz continuous gradient · Xingyu Zhou's blog
https://xingyuzhou.org
Hi Xingyu, strong convexity is a sub-condition of the PL inequality and hence by order of transitivity must imply Lipschitz continuous gradient.
Chapter 3 Gradient
https://web.eecs.umich.edu
Lipschitz continuity of ∇f is a stronger condition than mere continuity, so any differentiable function whose gradient is Lipschitz continuous is in fact a ...
Lipschitz continuity
https://en.wikipedia.org
In mathematical analysis, Lipschitz continuity, named after German mathematician Rudolf Lipschitz, is a strong form of uniform continuity for functions.
Is a Lipschitz continuous gradient equivalent to this ...
https://mathoverflow.net
I know if a function f:Rn→R is L-smooth, i.e. its gradient ∇f is L-Lipschitz continuous, then it satisfies the following inequality for any x, ...
Lipschitz continuous gradient and quadratic bound property
https://math.stackexchange.com
A standard result is that a function f (not necessarily convex) with Lipschitz continuous gradient satisfies the following quadratic bound ...
Notes on Convex Optimization Gradient Descent
https://chunpai.github.io
Lipschitz Continuous Gradient: gradient of f is Lipschitz continuous with parameter L ≥ 0 if. ||∇f(x) − ∇f(y)||2 ≤ L||x − y||2. ∀x, y ∈ dom(f). (18).
Inequality of convex function with Lipschitz continuous ...
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Inequality for convex function say f with L-Lipschitz continuous gradient: (x−y)T(α∇f(x)−β∇f(y))?