A proximal limited-memory quasi-Newton scheme is developed for nonsmooth nonconvex optimization, with global convergence proven under mild assumptions and rates under the Kurdyka-Lojasiewicz property.
Mordukhovich.Variational Analysis and Applications, volume 30
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Approximate directional stationarity is formulated as a necessary optimality condition for nonsmooth constrained problems, with a qualification condition using one sequence to infer directional stationarity.
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Proximal Limited-Memory Quasi-Newton Methods for Nonsmooth Nonconvex Optimization
A proximal limited-memory quasi-Newton scheme is developed for nonsmooth nonconvex optimization, with global convergence proven under mild assumptions and rates under the Kurdyka-Lojasiewicz property.
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Approximate directional stationarity and associated qualification conditions
Approximate directional stationarity is formulated as a necessary optimality condition for nonsmooth constrained problems, with a qualification condition using one sequence to infer directional stationarity.