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Proximal Point Method on Finslerian Manifolds and the "Effort-Accuracy" Trade-off

Abstract : In this paper, we consider minimization problems with constraints. We show that, if the set of constraints is a Finslerian manifold of non-positive flag curvature, and the objective function is differentiable and satisfies the Kurdyka-Lojasiewicz property, then the proximal point method can be naturally extended to solve this class of problems. We prove that the sequence generated by our method is well defined and converges to a critical point. We show how tools of Finslerian geometry, specifically non-symmetrical metrics, can be used to solve non-convex constrained problems in Euclidean spaces. As an application, we give one result regarding decision-making speed and costs related to change.
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https://hal-amu.archives-ouvertes.fr/hal-01474289
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Submitted on : Wednesday, February 22, 2017 - 4:27:17 PM
Last modification on : Wednesday, August 5, 2020 - 3:15:03 AM

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Joao Xavier Cruz Neto, Paulo Roberto Oliveira, Jr Soares, Antoine Soubeyran. Proximal Point Method on Finslerian Manifolds and the "Effort-Accuracy" Trade-off. Journal of Optimization Theory and Applications, Springer Verlag, 2014, 162 (3), pp.873--891. ⟨10.1007/s10957-013-0483-5⟩. ⟨hal-01474289⟩

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