Approximating a common zero of finite family of monotone operators in Hadamard spaces

In this paper, a common zero of a finite family of monotone operators is approximated in Hadamard spaces. Some applications in convex minimization and fixed point theory are also presented.     

Matrix approaches to approximate solutions of variational inequalities in Hilbert spaces

A matrix approach to approximating solutions of variational inequalities in Hilbert spaces is introduced. This approach uses two matrices: one for iteration process and the other for regularization. Ergodicity and convergence (both weak and strong) are studied. Our methods combine new or well-known iterative methods (such as the original Mann’s method) with regularized processes involved regular matrices in the sense of Toeplitz.     

Subgradient algorithms on Riemannian manifolds of lower bounded curvatures

The subgradient algorithms for convex optimizations on Riemannian Manifolds of sectional curvatures bounded from below are studied; and the convergence results of the algorithms (employing diminishing step sizes and dynamic step sizes) are established. Some numerical experiments are provided to illustrate the convergence performances of the algorithms.