• Corpus ID: 253761006

Descent modulus and applications

  title={Descent modulus and applications},
  author={Aris Daniilidis and Laurent Miclo and David Salas},
. The norm of the gradient k∇ f ( x ) k measures the maximum descent of a real-valued smooth function f at x . For (nonsmooth) convex functions, this is expressed by the distance dist(0 , ∂f ( x )) of the subdifferential to the origin, while for general real-valued functions defined on metric spaces by the notion of metric slope |∇ f | ( x ). In this work we propose an axiomatic definition of descent modulus T [ f ]( x ) of a real-valued function f at every point x , defined on a general (not… 

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