subdifferentiable mapping

Let X be a Banach space, and let X* be the dual space of X. For a function f:X, and xX, let us define

f(x)={r*X*:f(x)-f(y)r(x-y)for allyX}.

If f(x) is non-empty, then f is subdifferentiable at xX, and if f(x) is non-empty for all x, then f is subdifferentiable [1, 2].


  • 1 C. Zalinescu, Convex Analysis in General Vector Spaces, World Scientific Publishing Company, 2002.
  • 2 R.T. Rockafellar, Convex Analysis, Princeton University Press, 1996.
Title subdifferentiable mapping
Canonical name SubdifferentiableMapping
Date of creation 2013-03-22 14:31:19
Last modified on 2013-03-22 14:31:19
Owner matte (1858)
Last modified by matte (1858)
Numerical id 13
Author matte (1858)
Entry type Definition
Classification msc 39B62
Classification msc 52-00