We disclose an interesting connection between the gradient flow of a C
2
-
smooth function ψ and evanescent orbits of the second order gradient system defined
by the square-norm of ∇ψ, under adequate convexity assumption. As a consequence,
we obtain the following surprising result for two C
2
, convex and bounded from below
functions ψ1, ψ2: if ||∇ψ1|| = ||∇ψ2||, then ψ1 = ψ2 + k, for some k ∈ R
Lenguage
dc.language.iso
en
Publisher
dc.publisher
Society for Industrial and Applied Mathematics Publications