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We present a smoothing projected Barzilai–Borwein (SPBB) algorithm for solving a class of minimization problems on a closed convex set, where the objective function is nonsmooth nonconvex, perhaps even non-Lipschitz. At each iteration, the SPBB algorithm applies the projected gradient strategy that alternately uses the two Barzilai–Borwein stepsizes to the smooth approximation of the original problem...
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