14 citations · 31 across the 22 of their papers we have counts for
22 papers
Subgradient Methods on Manifolds with Lower Bounded Curvature
G. C. Bento, J. X. Cruz Neto, J. O. Lopes +1
The subgradient method is a classical and foundational approach in non-smooth convex optimization; its simplicity, robustness, and role as a conceptual and algorithmic starting poi…
Convergence of Descent Optimization Algorithms under Polyak-Łojasiewicz-Kurdyka Conditions
G. C. Bento, B. S. Mordukhovich, T. S. Mota +1
This paper develops a comprehensive convergence analysis for generic classes of descent algorithms in nonsmooth and nonconvex optimization under several conditions of the Polyak-Ło…
A Refined Proximal Algorithm for Nonconvex Multiobjective Optimization in Hilbert Spaces
G. C. Bento, J. X. Cruz Neto, J. O. Lopes +2
This paper is devoted to general nonconvex problems of multiobjective optimization in Hilbert spaces. Based on Mordukhovich's limiting subgradients, we define a new notion of Paret…
Elements of Convex Geometry in Hadamard Manifolds with Application to Equilibrium Problems
G. C. Bento, J. X. Cruz Neto, I. D. L. Melo
In this paper, is introduced a new proposal of resolvent for equilibrium problems in terms of the Busemann's function. A great advantage of this new proposal is that, in addition t…
An inexact proximal point method for variational inequality on Hadamard manifolds
G. C. Bento, O. P. Ferreira, E. A. Papa Quiroz
In this paper we present an inexact proximal point method for variational inequality problem on Hadamard manifolds and study its convergence properties. The proposed algorithm is i…
An Extragradient-type Algorithm for Variational Inequality on Hadamard Manifolds
E. E. A. Batista, G. C. Bento, O. P. Ferreira
The aim of this paper is to present an extragradient method for variational inequality associated to a point-to-set vector field in Hadamard manifolds and to study its convergence…
Iteration-complexity of gradient, subgradient and proximal point methods on Riemannian manifolds
G. C. Bento, O. P. Ferreira, J. G. Melo
This paper considers optimization problems on Riemannian manifolds and analyzes iteration-complexity for gradient and subgradient methods on manifolds with non-negative curvature.…
Enlargement of Monotone Vector Fields and an Inexact Proximal Point Method for Variational Inequalities in Hadamard Manifolds
E. E. A. Batista, G. C. Bento, O. P. Ferreira
In this paper an inexact proximal point method for variational inequalities in Hadamard manifolds is introduced and studied its convergence properties. The main tool used for prese…
Existence Results for Particular Instances of the Vector Quasi-Equilibrium Problem on Hadamard Manifolds
G. C. Bento, J. X. Cruz Neto
We show the validity of select existence results for a vector optimization problem, and a variational inequality. More generally, we consider generalized vector quasi-variational i…
Proximal point method for a special class of nonconvex multiobjective optimization functions
G. C. Bento, O. P. Ferreira, V. L. Sousa Junior
The proximal point method for a special class of nonconvex multiobjective functions is studied in this paper. We show that the method is well defined and that the accumulation poin…
A proximal point algorithm with generalized proximal distances to BEPs
G. C. Bento, J. X. Cruz Neto, J. O. Lopes +2
We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a proximal point method with generalized proximal distan…
An Existence Result for the Generalized Vector Equilibrium Problem on Hadamard Manifold
E. E. A. Batista, G. C. Bento, O. P. Ferreira
A sufficient condition for the existence of a solution for generalized vector equilibrium problem (GVEP) on Hadamard manifold, by using a version of KKM lemma on this context, is p…
Some comparisons between the Variational rationality, Habitual domain, and DMCS approaches
G. C. Bento, A. Soubeyran
The "Habitual domain" (HD) approach and the "Variational rationality" (VR) approach belong to the same strongly interdisciplinary and very dispersed area of research: human stabili…
Proximal algorithms with Bregman distances for bilevel equilibrium problems with application to the problem of "how routines form and change" in Economics and Management Sciences
G. C. Bento, J. X. Cruz Neto, P. A. Soares +1
In this paper we present the bilevel equilibrium problem under conditions of pseudomonotonicity. Using Bregman distances on Hadamard manifolds we propose a framework for to analyse…
Behavioral Traps and the Equilibrium Problem on Hadamard Manifolds
G. C. Bento, J. X. Cruz Neto, P. A. Soares +1
In this paper we present a sufficient condition for the existence of a solution for an equilibrium problem on an Hadamard manifold and under suitable assumptions on the sectional c…
Generalized Inexact Proximal Algorithms: Habit's/ Routine's Formation with Resistance to Change, following Worthwhile Changes
G. C. Bento, A. Soubeyran
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, Eco…
The inexact projected gradient method for quasiconvex vector optimization problems
J. Y. Bello Cruz, G. C. Bento, G. Bouza Allende +1
Vector optimization problems are a generalization of multiobjective optimization in which the preference order is related to an arbitrary closed and convex cone, rather than the no…
Weak Sharp Minima and Finite Termination of the Proximal Point Method for Convex Functions on Hadamard Manifolds
G. C. Bento, J. X. da Cruz Neto
In this paper we proved that the sequence generated by the proximal point method, associated to a unconstrained optimization problem in the Riemannian context, has finite terminati…
Convergence of inexact descent methods for nonconvex optimization on Riemannian manifolds
G. C. Bento, J. X. da Cruz Neto, P. R. Oliveira
In this paper we present an abstract convergence analysis of inexact descent methods in Riemannian context for functions satisfying Kurdyka-Lojasiewicz inequality. In particular, w…
Unconstrained steepest descent method for multicriteria optimization on Riemmanian manifolds
G. C. Bento, O. P. Ferreira, P. R. Oliveira
In this paper we present a steepest descent method with Armijo's rule for multicriteria optimization in the Riemannian context. The well definedness of the sequence generated by th…
Local Convergence of the Proximal Point Method for a Special Class of Nonconvex Functions on Hadamard Manifolds
G. C. Bento, O. P. Ferreira, P. R. Oliveira
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 sequenc…
Proximal Point Method for a Special Class of Nonconvex Functions on Hadamard Manifolds
G. C. Bento, O. P. Ferreira, P. R. Oliveira
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…