## Visualization of the $$\varepsilon$$-subdifferential of piecewise linear-quadratic functions.(English)Zbl 1406.90092

Summary: Computing explicitly the $$\varepsilon$$-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.

### MSC:

 90C25 Convex programming 90C20 Quadratic programming

### Software:

PLCP; Scilab; SQPlab; CCA
Full Text:

### References:

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