arXiv 1709.082392017-09-24math.OC

Visualization of the ε-Subdifferential of Piecewise Linear-Quadratic Functions

Anuj Bajaj, Warren Hare, Yves Lucet

发表信息：: Computational Optimization and Applications 2017 67(2) 421-442
DOI：: 10.1007/s10589-017-9892-y

英文摘要：

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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