We introduce an iterative procedure for finding a point in the zero set (a solution to 0 ∈ A(v) and v ∈ C) of an inverse-monotone or inverse strongly-monotone operator A on a nonempty closed convex subset C in a uniformly smooth and uniformly convex Banach space. We establish weak convergence results under suitable assumptions.

In this paper, we present a new type of extra-gradient method for generalized variational inequalities with multi-valued mapping in an infinite-dimensional Hilbert space. For this method, the generated sequence possesses an expansion property with respect to the initial point, and the existence of the solution to the problem can be verified through the behavior of the generated sequence. Furthe...

and Applied Analysis 3 2. Preliminaries Let H be a real Hilbert space with inner product 〈·, ·〉 and norm ‖ · ‖, and let C be a closed convex subset of H. It is well known that, for any u ∈ H, there exists a unique u0 ∈ C such that ‖u − u0‖ inf{‖u − x‖ : x ∈ C}. 2.1 We denote u0 by PCu, where PC is called the metric projection of H onto C. The metric projection PC ofH onto C has the following ba...

and Applied Analysis 3 2. Preliminaries Let C be a nonempty closed convex subset of a real Banach space E. Recall that a mapping A of C into E is said to be accretive if there exists j x − y ∈ J x − y such that 〈 Ax −Ay, j(x − y)〉 ≥ 0, 2.1 for all x, y ∈ C. A mapping A of C into E is said to be α-strongly accretive if, for α > 0, 〈 Ax −Ay, j(x − y)〉 ≥ α∥∥x − y∥∥2, 2.2 for all x, y ∈ C. A mappin...

We develop a new stochastic algorithm for solving pseudomonotone variational inequalities. Our method builds on Tseng’s forward-backward-forward algorithm, which is known in the deterministic literature to be valuable alternative Korpelevich’s extragradient when inequalities over convex and closed set governed by Lipschitz continuous operators. The main computational advantage of that it relies...

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This article considers the generalized (two-player) Nash equilibrium (GNE) problem with a separable non-smooth part, which is known to include the generalized saddle-point (GSP) problem as a special case. Due to its two-block structure, this problem can be solved by any algorithm belonging to the block-decomposition hybrid proximal-extragradient framework proposed in [13]. The framework consist...