Many modern machine learning applications-from online principal component analysis to
covariance matrix identification and dictionary learning-can be formulated as minimization …

Many important learning algorithms, such as stochastic gradient methods, are often
deployed to solve nonlinear problems on Riemannian manifolds. Motivated by these …

The Equilibrium problem (EP) was early introduced by Fan [11] which is also known as the
Fan's inequality and extensively developed by Blum and Oettli [3]. It plays a very important …

This paper presents an extragradient method for variational inequality associated with a
point-to-set vector field in Hadamard manifolds, and a study of its convergence properties …

In this work, we are concerned with the iterative approximation of solutions to equilibrium
problems in the framework of Hadamard manifolds. We introduce a subgradient …

In this paper, we introduce a new proximal algorithm for equilibrium problems on a genuine
Hadamard manifold, using a new regularization term. We first extend recent existence …

In this paper, we introduce three adaptive extragradient-based algorithms for solving
equilibrium problems in Hadamard manifolds. The proposed algorithms can work adaptively …

We examine a wide class of stochastic approximation algorithms for solving (stochastic)
nonlinear problems on Riemannian manifolds. Such algorithms arise naturally in the study …

This paper presents an extragradient-like method for solving a pseudomonotone equilibrium
problem with a Lipschitz-type condition on Hadamard manifolds. The algorithm only needs …

In this paper, we present two algorithms for solving equilibrium problems on Hadamard
manifolds. The two algorithms use the extragradient model and the golden ratio model …