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Visualization of the ε-subdifferential of piecewise linear-quadratic functions Bajaj, Anuj; Hare, Warren; Lucet, Yves
Abstract
Computing explicitly the 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.
Item Metadata
Title |
Visualization of the ε-subdifferential of piecewise linear-quadratic functions
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Creator | |
Publisher |
Springer
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Date Issued |
2017
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Description |
Computing explicitly the 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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Subject | |
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Type | |
Language |
eng
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Date Available |
2019-07-17
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0379905
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URI | |
Affiliation | |
Citation |
Bajaj, A., Hare, W., & Lucet, Y. (2017). Visualization of the ε-subdifferential of piecewise linear-quadratic functions. Computational Optimization and Applications, 67(2), 421.
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Publisher DOI |
10.1007/s10589-017-9892-y
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Peer Review Status |
Reviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International