Iteration-complexity of gradient, subgradient and proximal point methods on Riemannian manifolds

GC Bento, OP Ferreira, JG Melo - Journal of Optimization Theory and …, 2017 - Springer
This paper considers optimization problems on Riemannian manifolds and analyzes the
iteration-complexity for gradient and subgradient methods on manifolds with nonnegative …

ε-subgradient algorithms for locally lipschitz functions on Riemannian manifolds

P Grohs, S Hosseini - Advances in Computational Mathematics, 2016 - Springer
This paper presents a descent direction method for finding extrema of locally Lipschitz
functions defined on Riemannian manifolds. To this end we define a set-valued mapping …

The KKT optimality conditions for optimization problem with interval-valued objective function on Hadamard manifolds

S Chen - Optimization, 2022 - Taylor & Francis
In this paper, we study the Karush–Kuhn–Tucker optimality conditions in an optimization
problem with interval-valued objective function on Hadamard manifolds. The gH-directional …

Global error bounds for mixed quasi-hemivariational inequality problems on Hadamard manifolds

NV Hung, VM Tam, A Pitea - Optimization, 2020 - Taylor & Francis
In this paper, we introduce and study a class of mixed quasi-hemivariational inequality
problems on Hadamard manifolds (in short,(MQHIP)). Some regularized gap functions for …

Proximal point algorithm for inclusion problems in Hadamard manifolds with applications

QH Ansari, F Babu - Optimization Letters, 2021 - Springer
This paper deals with the proximal point algorithm for finding a singularity of sum of a single-
valued vector field and a set-valued vector field in the setting of Hadamard manifolds. The …

Local convergence of the proximal point method for a special class of nonconvex functions on Hadamard manifolds

GC Bento, OP Ferreira, PR Oliveira - Nonlinear Analysis: Theory, Methods …, 2010 - Elsevier
Local convergence analysis of the proximal point method for a special class of nonconvex
functions on Hadamard manifold is presented in this paper. The well definedness of the …

Nonsmooth trust region algorithms for locally Lipschitz functions on Riemannian manifolds

P Grohs, S Hosseini - IMA Journal of Numerical Analysis, 2016 - academic.oup.com
This paper presents a Riemannian trust region algorithm for unconstrained optimization
problems with locally Lipschitz objective functions defined on complete Riemannian …

Applications of a variable anchoring iterative method to equation and inclusion problems on Hadamard manifolds

DR Sahu, A Pitea, S Sharma, AK Singh - Communications in Nonlinear …, 2024 - Elsevier
In this paper, we introduce a new iterative technique with a variable anchoring operator for
reckoning the solution of a variational inequality problem over the set of the common fixed …

Convergence analysis of a proximal point algorithm for minimizing differences of functions

NT An, NM Nam - Optimization, 2017 - Taylor & Francis
Several optimization schemes have been known for convex optimization problems.
However, numerical algorithms for solving nonconvex optimization problems are still …

Levitin–Polyak well-posedness by perturbations for the split hemivariational inequality problem on Hadamard manifolds

VM Tam, N Van Hung, Z Liu, JC Yao - Journal of Optimization Theory and …, 2022 - Springer
The purpose of this paper is to establish some new results on the Levitin–Polyak well-
posedness to a class of split hemivariational inequality problems on Hadamard manifolds …