English

Visualization of the {\epsilon}-Subdifferential of Piecewise Linear-Quadratic Functions

Optimization and Control 2017-09-26 v1

Abstract

Computing explicitly the {\epsilon}-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 Br{\o}ndsted-Rockafellar Theorem.

Keywords

Cite

@article{arxiv.1709.08239,
  title  = {Visualization of the {\epsilon}-Subdifferential of Piecewise Linear-Quadratic Functions},
  author = {Anuj Bajaj and Warren Hare and Yves Lucet},
  journal= {arXiv preprint arXiv:1709.08239},
  year   = {2017}
}