# Visualization of the $$\varepsilon$$ ε -subdifferential of piecewise linear–quadratic functions

## Author Info

Listed author(s):
• Anuj Bajaj

()

(Wayne State University)

• Warren Hare

()

(The University of British Columbia - Okanagan (UBCO))

• Yves Lucet

()

(The University of British Columbia - Okanagan (UBCO))

Registered author(s):

## Abstract

Abstract Computing explicitly the $$\varepsilon$$ 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.

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## Bibliographic Info

Article provided by Springer in its journal Computational Optimization and Applications.

Volume (Year): 67 (2017)
Issue (Month): 2 (June)
Pages: 421-442

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 Handle: RePEc:spr:coopap:v:67:y:2017:i:2:d:10.1007_s10589-017-9892-y DOI: 10.1007/s10589-017-9892-y Contact details of provider: Web page: http://www.springer.com Order Information: Web: http://www.springer.com/math/journal/10589

## References

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1. Bryan Gardiner & Khan Jakee & Yves Lucet, 2014. "Computing the partial conjugate of convex piecewise linear-quadratic bivariate functions," Computational Optimization and Applications, Springer, vol. 58(1), pages 249-272, May.
2. Yves Lucet & Heinz Bauschke & Mike Trienis, 2009. "The piecewise linear-quadratic model for computational convex analysis," Computational Optimization and Applications, Springer, vol. 43(1), pages 95-118, May.
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