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Solver-o-matic

"These days, even the most pure and abstract mathematics is in danger to be applied."
- Anonymous

Decision Tree for Nonsmooth Optimization Software

Your first choice should be Quasi-Secant Method (QSM) with discrete gradients. QSM is a solver for nonsmooth possibly nonconvex minimization by A. Bagirov and A. Ganjehlou. In QSM one can employ either analytically calculated or approximated subgradients (this can be done automatically by selecting one parameter). The Fortran 77 source code of QSM is available for downloading.

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