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Proximal Point Method for Minimizing Quasiconvex Locally Lipschitz Functions on Hadamard Manifolds

Erik Alex Papa Quiroz(erikpapa***at***gmail.com)
Paulo Roberto Oliveira(poliveir***at***cos.ufrj.br)

Abstract: In this paper we propose an extension of the proximal point method to solve minimization problems with quasiconvex locally Lipschitz objective functions on Hadamard manifolds. To reach this goal, we use the concept of Clarke subdifferential on Hadamard manifolds and assuming that the function is bounded from below, we prove the global convergence of the sequence generated by the method to a critical point of the function.

Keywords: Proximal point method, quasiconvex functions, locally Lipschitz functions, Hadamard manifolds, global convergence.

Category 1: Global Optimization


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Entry Submitted: 02/07/2012
Entry Accepted: 02/08/2012
Entry Last Modified: 02/07/2012

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