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The $\epsilon$-subdifferential of convex univariate piecewiselinear-quadratic functions can be computed in linear worst-case time complexityas the level-set of a convex function. Using dichotomic search, we show how thecomputation can be performed in logarithmic worst-case time. Furthermore, a newalgorithm to compute the entire graph of the $\epsilon$-subdifferential inlinear time is presented. Both algorithms are not limited to convex PLQfunctions but are also applicable to any convex piecewise-defined function withlittle restrictions.

Computation of the Epsilon-Subdifferential of Convex Piecewise-Defined Functions in Optimal Worst-Case Time