Finite-valued infimal convolution
= Finite-valued infimal convolution
If two nonnegative finite-valued <convex functions> are defined on all of a finite-dimensional space, their <infimal convolution> is finite, <convex> and continuous everywhere. <Convex perturbation duality> then gives <strong duality> and dual attainment at every argument. It does not require or imply attainment of the primal decomposition infimum.