8 citations · 29 across the 50 of their papers we have counts for
40 papers · 1 filter
Projected Gradient Method on Hadamard Manifolds
O. P. Ferreira, M. L. N. Gonçalves, A. M. González +1
We study constrained smooth optimization problems on Hadamard manifolds with closed geodesically convex feasible sets. We analyze two projected gradient schemes: one with a constan…
Ball-proximal point method on a Hadamard Manifolds
F. Babu, O. P. Ferreira, L. F. Prudente +2
We consider the problem of minimizing a proper, lower semicontinuous, geodesically convex function on a Hadamard manifold. Building on ball-proximal (broximal) ideas in the Euclide…
A Busemann hybrid projection-proximal point algorithm for optimization problems on Hadamard manifolds
R. Díaz Millán, O. P. Ferreira, M. S. Louzeiro +1
We study optimization problems on Hadamard manifolds, motivated by recent advances in geometric approaches to optimization on curved spaces, particularly those involving the struct…
A subdifferential characterization via Busemann functions and applications to DC optimization on Hadamard manifolds
O. P. Ferreira, D. S. Gonçalves, M. S. Louzeiro +2
This paper investigates the properties of Busemann functions on Hadamard manifolds and their use in optimization algorithms in Riemannian settings. We present a new Busemann-based…
Broyden quasi-Newton secant-type method for solving constrained mixed generalized equations
P. C. da Silva Junior, O. P. Ferreira, G. N. Silva
This paper presents a novel variant of the Broyden quasi-Newton secant-type method aimed at solving constrained mixed generalized equations, which can include functions that are no…
Frank--Wolfe algorithms for piecewise star-convex functions with a nonsmooth difference-of-convex structure
R. Díaz Millán, O. P. Ferreira, J. Ugon
In the present paper, we formulate two versions of Frank--Wolfe algorithm or conditional gradient method to solve the DC optimization problem with an adaptive step size. The DC obj…
Constraint qualifications and strong global convergence properties of an augmented Lagrangian method on Riemannian manifolds
Roberto Andreani, Kelvin Rodrigues Couto, Orizon Pereira Ferreira +1
In the past years, augmented Lagrangian methods have been successfully applied to several classes of non-convex optimization problems, inspiring new developments in both theory and…
A generalized conditional gradient method for multiobjective composite optimization problems
P. B. Assunção, O. P. Ferreira, L. F. Prudente
This article deals with multiobjective composite optimization problems that consist of simultaneously minimizing several objective functions, each of which is composed of a combina…
Introducao a otimizacao de Portfolio
Orizon P. Ferreira, Guilherme. A. Franca, Max V. Lemes
In this work, we introduce Modern Portfolio Theory using basic concepts from linear algebra, differential calculus, statistics, and optimization. This theory allows us to measure t…
The difference of convex algorithm on Hadamard manifolds
Ronny Bergmann, Orizon P. Ferreira, Elianderson M. Santos +1
In this paper, we propose a Riemannian version of the difference of convex algorithm (DCA) to solve a minimization problem involving the difference of convex (DC) function. We esta…
A boosted DC algorithm for non-differentiable DC components with non-monotone line search
Orizon P. Ferreira, Elianderson M. Santos, João Carlos O. Souza
We introduce a new approach to apply the boosted difference of convex functions algorithm (BDCA) for solving non-convex and non-differentiable problems involving difference of two…
Convexity of sets and quadratic functions on the hyperbolic space
Orizon Pereira Ferreira, Sándor Zoltán Németh, Jinzhen Zhu
In this paper some concepts of convex analysis on hyperbolic space are studied. We first study properties of the intrinsic distance, for instance, we present the spectral decomposi…
On the inexact scaled gradient projection method
Orizon P. Ferreira, Max V. Lemes, Leandro F. Prudente
The purpose of this paper is to present an inexact version of the scaled gradient projection method on a convex set, which is inexact in two sense. First, an inexact projection on…
Boosted scaled subgradient method for DC programming
Orizon P. Ferreira, Elianderson M. Santos, João Carlos O. Souza
The purpose of this paper is to present a boosted scaled subgradient-type method (BSSM) to minimize the difference of two convex functions (DC functions), where the first function…
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…
Inexact gradient projection method with relative error tolerance
Ademir A. Aguiar, Orizon P. Ferreira, Leandro F. Prudente
A gradient projection method with feasible inexact projections is proposed in the present paper. The inexact projection is performed using a relative error tolerance. Asymptotic co…
Iteration-complexity and asymptotic analysis of steepest descent method for multiobjective optimization on Riemannian manifolds
Orizon P. Ferreira, Maurício S. Louzeiro, Leandro F. Prudente
The steepest descent method for multiobjective optimization on Riemannian manifolds with lower bounded sectional curvature is analyzed in this paper. The aim of the paper is twofol…
On the spherical quasi-convexity of quadratic functions on spherical self-dual convex sets
Orizon P. Ferreira, Sándor Z. Németh, Lianghai Xiao
In this paper, the spherical quasi-convexity of quadratic functions on spherically subdual convex sets is studied. Sufficient conditions for spherical quasi-convexity on sphericall…
Newton method for finding a singularity of a special class of locally Lipschitz continuous vector fields on Riemannian manifolds
Fabiana R. de Oliveira, Orizon P. Ferreira
In this paper, we extend some results of nonsmooth analysis from Euclidean context to the Riemannian setting. In particular, we discuss the concept and some properties of locally L…
Iteration-Complexity of the Subgradient Method on Riemannian Manifolds with Lower Bounded Curvature
O. P. Ferreira, M. S. Louzeiro, L. F. Prudente
The subgradient method for convex optimization problems on complete Riemannian manifolds with lower bounded sectional curvature is analyzed in this paper. Iteration-complexity boun…
Gradient Method for Optimization on Riemannian Manifolds with Lower Bounded Curvature
O. P. Ferreira, M. S. Louzeiro, L. F. Prudente
The gradient method for minimize a differentiable convex function on Riemannian manifolds with lower bounded sectional curvature is analyzed in this paper. The analysis of the meth…
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…
On the spherical quasi-convexity of quadratic functions
O. P. Ferreira, S. Z. Németh, L. Xiao
In this paper the spherical quasi-convexity of quadratic functions on spherically convex sets is studied. Several conditions characterizing the spherical quasi-convexity of quadrat…
Damped Newton's Method on Riemannian Manifolds
M. A. A. Bortoloti, T. A. Fernandes, O. P. Ferreira +1
A damped Newton's method to find a singularity of a vector field in Riemannian setting is presented with global convergence study. It is ensured that the sequence generated by the…