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Active strict saddles in nonsmooth optimization

Damek Davis(dsd95***at***cornell.edu)
Dmitriy Drusvyatskiy(ddrusv***at***uw.edu)

Abstract: We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We argue that the strict saddle property may be a realistic assumption in applications, since it provably holds for generic semi-algebraic optimization problems.

Keywords: strict saddles, active manifolds, proximal algorithms, Kurdyka Lojasiewicz property

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )


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Entry Submitted: 12/15/2019
Entry Accepted: 12/15/2019
Entry Last Modified: 12/15/2019

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