Gradient Lipschitz continuous：1. Gradient method
1. Gradient method
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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).
Gradient Descent
https://www.stat.cmu.edu
I.e., ∇f is Lipschitz continuous with constant L > 0. Theorem: Gradient descent with fixed step size t ≤ 1/L satisfies f(x(k)) − f? ≤ kx(0) − x?k2. 2. 2tk.
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))?