4 citations · 13 across the 14 of their papers we have counts for
15 papers
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…
A Second-Order Algorithm Based on Affine Scaling Interior-Point Methods for nonlinear Optimisation with bound constraints
Yonggang Pei, Yubing Lin, Mauricio Silva Louzeiro +1
The homogeneous second-order descent method (Zhang et al. 2025, Mathematics of Operations Research) was initially proposed for unconstrained optimisation problems. HSODM shows exce…
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…
A Riemannian AdaGrad-Norm Method
Glaydston de C. Bento, Geovani N. Grapiglia, Mauricio S. Louzeiro +1
We propose a manifold AdaGrad-Norm method (\textsc{MAdaGrad}), which extends the norm version of AdaGrad (AdaGrad-Norm) to Riemannian optimization. In contrast to line-search schem…
A scalable sequential adaptive cubic regularization algorithm for optimization with general equality constraints
Yonggang Pei, Yubing Lin, Shuai Shao +2
The scalable adaptive cubic regularization method (: Dussault et al. in Math. Program. Ser. A 207(1-2): 191-225, 2024) has been recently proposed for unconstrain…
An Adaptive Cubic Regularization quasi-Newton Method on Riemannian Manifolds
Mauricio S. Louzeiro, Gilson N. Silva, Jinyun Yuan +1
A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at m…
Inexact Newton Methods for Solving Generalized Equations on Riemannian Manifolds
Mauricio S. Louzeiro, Gilson N. Silva, Jinyun Yuan +1
The convergence of inexact Newton methods is studied for solving generalized equations on Riemannian manifolds by using the metric regularity property, which is also explored. Unde…
A Projected Subgradient Method for the Computation of Adapted Metrics for Dynamical Systems
Maurício Louzeiro, Christoph Kawan, Sigurdur Hafstein +2
In this paper, we extend a recently established subgradient method for the computation of Riemannian metrics that optimizes certain singular value functions associated with dynamic…
First- and Second-Order Analysis for Optimization Problems with Manifold-Valued Constraints
Ronny Bergmann, Roland Herzog, Julián Ortiz López +1
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the cod…
Fenchel Duality and a Separation Theorem on Hadamard Manifolds
Maurício Silva Louzeiro, Ronny Bergmann, Roland Herzog
In this paper, we introduce a definition of Fenchel conjugate and Fenchel biconjugate on Hadamard manifolds based on the tangent bundle. Our definition overcomes the inconvenience…
Fenchel Duality Theory and A Primal-Dual Algorithm on Riemannian Manifolds
Ronny Bergmann, Roland Herzog, Maurício Silva Louzeiro +2
This paper introduces a new notion of a Fenchel conjugate, which generalizes the classical Fenchel conjugation to functions defined on Riemannian manifolds. We investigate its prop…
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…
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…