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}
}