Regularization methods for hierarchical variational inequality problems on Hadamard manifolds

Two-Step Methods for Variational Inequalities on Hadamard Manifolds

In this paper, we suggest and analyze a two-step method for solving the variational inequalities on Hadamard manifold using the auxiliary principle technique. The convergence of this new method requires only the partially relaxed strongly monotonicity, which is a weaker condition than monotonicity. Results can be viewed as refinement and improvement of previously known results.

Convergence of Variational Regularization Methods for Imaging on Riemannian Manifolds

We consider abstract operator equations Fu = y, where F is a compact linear operator between Hilbert spaces U and V , which are function spaces on closed, finite dimensional Riemannian manifolds, respectively. This setting is of interest in numerous applications such as Computer Vision and non-destructive evaluation. In this work, we study the approximation of the solution of the ill-posed oper...

Implicit Methods for Equilibrium Problems on Hadamard Manifolds

We use the auxiliary principle technique to suggest and analyze an implicit method for solving the equilibrium problems on Hadamard manifolds. The convergence of this new implicit method requires only the speudomonotonicity, which is a weaker condition than monotonicity. Some special cases are also considered.

Augmented Lagrangian methods for variational inequality problems

We introduce augmented Lagrangian methods for solving finite dimensional variational inequality problems whose feasible sets are defined by convex inequalities, generalizing the proximal augmented Lagrangian method for constrained optimization. At each iteration, primal variables are updated by solving an unconstrained variational inequality problem, and then dual variables are updated through ...

Explicit Iterative Method for Variational Inequalities on Hadamard Manifolds