## Computation of the epsilon-subdifferential of convex piecewise linear-quadratic functions in optimal worst-case time.(English)Zbl 07115099

Summary: The epsilon-subdifferential of convex univariate piecewise linear-quadratic (PLQ) functions can be computed in linear worst-case time complexity as the level-set of a convex function. Using binary search, we improve the complexity to logarithmic worst-case time, and prove such complexity is optimal. In addition, a new algorithm to compute the entire graph of the epsilon-subdifferential in (optimal) linear time is presented. Both algorithms are not limited to convex PLQ functions but are also applicable to any convex piecewise-defined functions with little restrictions.

### MSC:

 65K10 Numerical optimization and variational techniques

### Software:

na13; CCA ; SCAT; fenchel; na24
Full Text:

### References:

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