A Penalization-Gradient Algorithm for Variational Inequalities

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

Coupling Forward-Backward with Penalty Schemes and Parallel Splitting for Constrained Variational Inequalities

We are concerned with the study of a class of forward-backward penalty schemes for solving variational inequalities 0 ∈ Ax+NC(x) where H is a real Hilbert space, A : H ⇉ H is a maximal monotone operator, and NC is the outward normal cone to a closed convex set C ⊂ H. Let Ψ : H → R be a convex differentiable function whose gradient is Lipschitz continuous, and which acts as a penalization functi...

Prox-Penalization and Splitting Methods for Constrained Variational Problems

This paper is concerned with the study of a class of prox-penalization methods for solving variational inequalities of the form Ax + NC(x) 3 0 where H is a real Hilbert space, A : H ⇒ H is a maximal monotone operator and NC is the outward normal cone to a closed convex set C ⊂ H. Given Ψ : H → R ∪ {+∞} which acts as a penalization function with respect to the constraint x ∈ C, and a penalizatio...

Optimal Control of Problems Governed by Abstract Elliptic Variational Inequalities with State Constraints∗

In this paper we investigate optimal control problems governed by elliptic variational inequalities with additional state constraints. We present a relaxed formulation for the problem. With penalization methods and approximation techniques we give qualification conditions to get first-order optimality conditions.

On the Theory of Vector Optimization and Variational Inequalities. Image Space Analysis and Separation

By exploiting recent results, it is shown that the theories of Vector Optimization and of Vector Variational Inequalities can be based on the image space analysis and theorems of the alternative or separation theorems. It is shown that, starting from such a general scheme, several theoretical aspects can be developed – like optimality conditions, duality, penalization – as well as methods of so...