Glaydston de Carvalho Bento

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In this paper, following the ideas presented in Attouch et al. (Math. Program. Ser. A, 137: 91129, 2013), we present an inexact version of the proximal point method for nonsmoth functions, whose regularization is given by a generalized perturbation term. More precisely, the new perturbation term is defined as a “curved enough” function of the quasi distance(More)
Local convergence analysis of the proximal point method for special class of nonconvex function on Hadamard manifold is presented in this paper. The well definedness of the sequence generated by the proximal point method is guaranteed. Moreover, is proved that each cluster point of this sequence satisfies the necessary optimality conditions and, under(More)
In this paper, a subgradient type algorithm for solving convex feasibility problem on Riemannian manifold is proposed and analysed. The sequence generated by the algorithm converges to a solution of the problem, provided the sectional curvature of the manifold is non-negative. Moreover, assuming a Slater type qualification condition, we analyse a variant of(More)
This paper shows how, in a quasi metric space, an inexact proximal algorithm with a generalized perturbation term appears to be a nice tool for Behavioral Sciences (Psychology, Economics, Management, Game theory,. . . ). More precisely, the new perturbation term represents an index of resistance to change, defined as a “curved enough” function of the quasi(More)
In this paper we present the proximal point method for a special class of nonconvex function on a Hadamard manifold. The well definedness of the sequence generated by the proximal point method is guaranteed. Moreover, it is proved that each accumulation point of this sequence satisfies the necessary optimality conditions and, under additional assumptions,(More)
In this paper, a subgradient-type method for solving nonsmooth multiobjective optimization problems on Riemannian manifolds is proposed and analyzed. This method extends, to the multicriteria case, the classical subgradient method for real-valued minimization proposed by Ferreira and Oliveira (J. Optim. Theory Appl. 97:93–104, 1998). The sequence generated(More)