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Proximal point method on Finslerian manifolds and the "Effort Accuracy Trade off"

J. X. da Cruz Neto (jcruzneto***at***uol.com.br)
Paulo R. Oliveira (poliveir***at***cos.ufrj.br)
Pedro A. Soares Jr (pedrosoares***at***cos.ufrj.br)
Antoine Soubeyran (antoine.soubeyran***at***univmed.fr)

Abstract: In this paper we consider minimization problems with constraints. We will show that if the set of constraints is a Finslerian manifold of non positive flag curvature, and the objective function is di fferentiable and satisfi es the property Kurdyka-Lojasiewicz, then the proximal point method is naturally extended to solve that class of problems. We will prove that the sequence generated by our method is well de fined and converges to a minimizer point. We show how tools of Finslerian geometry, more speci fically non symmetrical metrics, can be used to solve nonconvex constrained problems in Euclidean spaces. As an application, we give one result on the speed of decision and making and costs to change.

Keywords: Proximal algorithms; Finslerian manifolds; nonconvex optimization; Kurdyka-Lojasiewicz inequality.

Category 1: Nonlinear Optimization

Category 2: Global Optimization (Applications )

Category 3: Applications -- Science and Engineering (Other )

Citation: PESC/COPPE - UFRJ - Rio de Janeiro, Brazil

Download: [PDF]

Entry Submitted: 08/12/2011
Entry Accepted: 08/12/2011
Entry Last Modified: 03/27/2012

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