On the Iteration Complexity of Some Projection Methods for Monotone Linear Variational Inequalities

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Projected Reflected Gradient Methods for Monotone Variational Inequalities

This paper is concerned with some new projection methods for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. First, we propose the projected reflected gradient algorithm with a constant stepsize. It is similar to the projected gradient method, namely, the method requires only one projection onto the feasible set and only one value of the ...

Generalized Projection Method for Non-lipschitz Multivalued Monotone Variational Inequalities

We generalize the projection method for solving strongly monotone multivalued variational inequalities when the cost operator is not necessarily Lipschitz. At each iteration at most one projection onto the constrained set is needed. When the convex constrained set is not polyhedral, we embed the proposed method in a polyhedral outer approximation procedure. This allows us to obtain the projecti...

A Modified Forward - Backward Splitting Methodfor Maximal Monotone

We consider the forward-backward splitting method for nding a zero of the sum of two maximal monotone mappings. This method is known to converge when the inverse of the forward mapping is strongly monotone. We propose a modiication to this method, in the spirit of the extragradient method for monotone variational inequalities, under which the method converges assuming only the forward mapping i...

A descent alternating direction method for monotone variational inequalities with separable structure

To solve a special class of variational inequalities with separable structure, this paper proposes a descent alternating direction method based on a new residual function. The most prominent characteristic of the method is that it is easily performed, in which, only some orthogonal projections and function evaluations are involved at each iteration, so its computational load is very tiny. Under...