Visualization of the ε-subdifferential of piecewise linear-quadratic functions

Computing explicitly the ε-subdifferential of a proper function amounts to computing the level set of a convex function namely the conjugate minus a linear function. The resulting theoretical algorithm is applied to the the class of (convex univariate) piecewise linear–quadratic functions for which existing numerical libraries allow practical computations. We visualize the results in a primal, dual, and subdifferential views through several numerical examples. We also provide a visualization of the Brøndsted–Rockafellar theorem.Arts and Sciences, Irving K. Barber School of (Okanagan)Computer Science, Mathematics, Physics and Statistics, Department of (Okanagan)ReviewedFacult