New First-Order Algorithms for Stochastic Variational Inequalities

Semistability of First-order Evolution Variational Inequalities

Semistability is the property whereby the solutions of a dynamical system converge to a Lyapunov stable equilibrium point determined by the system initial conditions. We extend the theory of semistability to a class of first-order evolution variational inequalities, and study the finite-time semistability. These results are Lyapunov-based and are obtained without any assumptions of sign definit...

First order algorithms in variational image processing

The success of non-smooth variational models in image processing is heavily based on efficient algorithms. Taking into account the specific structure of the models as sum of different convex terms, splitting algorithms are an appropriate choice. Their strength consists in the splitting of the original problem into a sequence of smaller proximal problems which are easy and fast to compute. Opera...

Confidence Regions for Stochastic Variational Inequalities

The sample average approximation (SAA) method is a basic approach for solving stochastic variational inequalities (SVI). It is well known that under appropriate conditions the SAA solutions provide asymptotically consistent point estimators for the true solution to an SVI. It is of fundamental interest to use such point estimators along with suitable central limit results to develop confidence ...

Iterative algorithms for families of variational inequalities fixed points and equilibrium problems

Iterative Algorithms for General Multivalued Variational Inequalities

and Applied Analysis 3 which is called the general variational inequality, introduced and studied by Noor 19 . It has been shown that the minimum of a class of differentiable functions can be characterized by the general variational inequality of type 2.3 . B If g ≡ I, the identity operator, then 2.1 reduces to find u ∈ C and w ∈ A u such that 〈F u w,v − u〉 ≥ 0, ∀v ∈ C, 2.4 which is known as th...