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

Author

Listed:
  • Anuj Bajaj

    () (Wayne State University)

  • Warren Hare

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

  • Yves Lucet

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

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.

Suggested Citation

  • Anuj Bajaj & Warren Hare & Yves Lucet, 2017. "Visualization of the $$\varepsilon $$ ε -subdifferential of piecewise linear–quadratic functions," Computational Optimization and Applications, Springer, vol. 67(2), pages 421-442, June.
  • Handle: RePEc:spr:coopap:v:67:y:2017:i:2:d:10.1007_s10589-017-9892-y
    DOI: 10.1007/s10589-017-9892-y
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    References listed on IDEAS

    as
    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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