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

Anuj Bajaj (), Warren Hare () and Yves Lucet ()
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Anuj Bajaj: Wayne State University
Warren Hare: The University of British Columbia - Okanagan (UBCO)
Yves Lucet: The University of British Columbia - Okanagan (UBCO)

Computational Optimization and Applications, 2017, vol. 67, issue 2, No 7, 442 pages

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.

Keywords: Subdifferentials; $$\varepsilon $$ ε -Subdifferentials; Computational convex analysis (CCA); Piecewise linear–quadratic functions; Convex function; Visualization (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10589-017-9892-y

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