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arXiv · 1709.08239

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

Anuj Bajaj·Warren Hare·Yves Lucet
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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.

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Anuj Bajaj, Warren Hare, Yves Lucet. 2017-09-24. Visualization of the {\epsilon}-Subdifferential of Piecewise Linear-Quadratic Functions. https://doi.org/10.1007/s10589-017-9892-y

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