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• W3102809253 abstract "In this paper, we present the nonconvex exterior-point operator splitting (NExOS) algorithm, a novel linearly convergent first-order algorithm tailored for constrained nonconvex learning problems. We consider the problem of minimizing a convex cost function over a nonconvex constraint set, where projection onto the constraint set is single-valued around local minima. A wide range of nonconvex learning problems have this structure including (but not limited to) sparse and low-rank optimization problems. By exploiting the underlying geometry of the constraint set, NExOS finds a locally optimal point by solving a sequence of penalized problems with strictly decreasing penalty parameters. NExOS solves each penalized problem by applying an outer iteration operator splitting algorithm, which converges linearly to a local minimum of the corresponding penalized formulation under regularity conditions. Furthermore, the local minima of the penalized problems converge to a local minimum of the original problem as the penalty parameter goes to zero. We implement NExOS in the open-source Julia package NExOS.jl, which has been extensively tested on many instances from a wide variety of learning problems. We study several examples of well-known nonconvex learning problems, and we show that in spite of being general purpose, NExOS is able to compute high quality solutions very quickly and is competitive with specialized algorithms." @default.
• W3102809253 created "2020-11-23" @default.
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• W3102809253 creator A5081461094 @default.
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• W3102809253 date "2020-11-09" @default.
• W3102809253 modified "2023-09-27" @default.
• W3102809253 title "Exterior-point Operator Splitting for Nonconvex Learning" @default.
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• W3102809253 hasPublicationYear "2020" @default.
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