It is well known that gap functions play a major role in developing error bounds for strongly monotone and affine monotone variational inequalities. However the error bound would be important from the point of view of computation if the gap function values diminishes on sequence of points which converge to a solution of the variational inequality. A gap function exhibiting such behavior is term...

Gamma and delta (gamma delta) T-cell receptor lymphocytes are increased during acute toxoplasmosis. These cells are BB3+ CD45RO+ CD8-. Purified gamma delta T cells failed to proliferate in response to Toxoplasma gondii antigen (stimulation index, 1.4 +/- 0.6) but were responsive to phytohemagglutinin stimulation (stimulation index, 20.8 +/- 1.9). Natural-killer-like cytotoxicity was strongly ac...

0. Introduction. Over the past thirty years, a powerful theory of monotone dynamical systems has been developed by many authors. A partial list of contributors would include N. Alikakos, E. N. Dancer, M. Hirsch, P. Hess, M.A. Krasnoselskii, U. Krause, H. Matano, P. Polacik, H.L. Smith, P. Takac and H. Thieme. If one understands the subject more generally as a chapter in the study of linear and ...

We propose and analyze the convergence of a novel stochastic algorithm for monotone inclusions that are sum of a maximal monotone operator and a single-valued cocoercive operator. The algorithm we propose is a natural stochastic extension of the classical forward-backward method. We provide a non-asymptotic error analysis in expectation for the strongly monotone case, as L. Rosasco DIBRIS, Univ...

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points F (S) of a nonexpansive mapping S and the set of solutions ΩA of the variational inequality for a monotone, Lipschitz continuous mapping A. We introduce a hybrid extragradient-like approximation method which is based on the well-known extragradient method and a hybrid (or outer approxi...

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...

We give in this paper a convergence result concerning parallel asynchronous algorithm with bounded delays to solve a nonlinear fixed point problems. This result is applied to calculate the solution of a strongly monotone operator. Special cases of these operators are used to solve some problems related to convex analysis like minimization of functionals, calculus of saddle point and variational...

The D-gap function has been useful in developing unconstrained descent methods for solving strongly monotone variational inequality problems. We show that the D-gap function has certain properties that are useful also for monotone variational inequality problems with bounded feasible set. Accordingly, we develop two unconstrained methods based on them that are similar in spirit to a feasible me...