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Inexact Proximal Point Methods for Quasiconvex Minimization on Hadamard Manifolds

Nancy Baygorrea (nbaygorrea***at***cos.ufrj.br)
Erik Papa Quiroz (erikpapa***at***gmail.com)
Nelson Maculan (maculan***at***cos.ufrj.br)

Abstract: In this paper we present two inexact proximal point algorithms to solve minimization problems for quasiconvex objective functions on Hadamard manifolds. We prove that under natural assumptions the sequence generated by the algorithms are well defined and converge to critical points of the problem. We also present an application of the method to demand theory in economy

Keywords: Proximal Point Method, Quasiconvex Function, Hadamard Manifolds, Nonsmooth Optimization, Abstract Subdifferential.

Category 1: Convex and Nonsmooth Optimization (Generalized Convexity/Monoticity )

Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 3: Global Optimization

Citation: Report optim 2015-1, PESC-UFRJ, Bloco H-Fundão, march 2015

Download: [PDF]

Entry Submitted: 03/03/2015
Entry Accepted: 03/03/2015
Entry Last Modified: 03/15/2015

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