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Forward-Backward Algorithms for Weakly Convex Problems
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DOI：10.1007/s00245-026-10420-4.png)
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Abstract
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We investigate the convergence properties of exact and inexact forward-backward algorithms to minimize the sum of two weakly convex functions defined on a Hilbert space, where one has a Lipschitz-continuous gradient. We show that the exact forward-backward algorithm locally converges strongly to a global solution, provided that the objective function satisfies a sharpness condition. For the inexact forward-backward algorithm, the same condition ensures that the distance from the iterates to the solution set approaches a positive threshold depending on the accuracy level of the proximal computations. As an application of the considered setting, we provide numerical experiments related to discrete tomography.
Keywords:
Weakly convex functions
Sharpness condition
Forward-backward algorithm
Inexact forward-backward algorithm
rho-Criticality
Proximal subgradient
Proximal operator
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1.7
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129
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0
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