In this paper, a new three-step iterative scheme is introduced for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality for α-inverse-strongly monotone mappings. The result reveals that the proposed iterative sequence converges strongly to the common element of this two. And our studies can be regarded as an extensi...

a general notion of completely monotone functionals on an ordered banach algebra b into a proper h*-algebra a with an integral representation for such functionals is given. as an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. a generalized version of bochner’s theorem on foundation se...

Abstract We introduce a dynamical system to the problem of finding zeros sum two maximally monotone operators. investigate existence, uniqueness and extendability solutions this in Hilbert space. prove that trajectories proposed converge strongly primal–dual solution considered problem. Under explicit time discretization we obtain best approximation algorithm for solving coupled inclusion

Abstract In this paper we discuss the optimal control of a quasilinear parabolic state equation. Its form is leaned on kind problems arising for example when controlling anisotropic Allen–Cahn equation as model crystal growth. Motivated by application consider result gradient flow an energy functional. The term strongly monotone and obeys certain growth condition lower order non-monotone. discr...

The majority of First Order methods for large-scale convex-concave saddle point problems and variational inequalities with monotone operators are proximal algorithms which at every iteration need to minimize over problem’s domain X the sum of a linear form and a strongly convex function. To make such an algorithm practical, X should be proximal-friendly – admit a strongly convex function with e...

Variational inequality methods whether based on numerous available new algorithms or otherwise have been applied vigorously, especially to model equilibria problems in economics, optimization and control theory, operations research, transportation network modeling, and mathematical programming, while a considerable progress to developing general methods for the sensitivity analysis for variatio...

This paper is a survey of methods for solving smooth (strongly) monotone stochastic variational inequalities. To begin with, we give the deterministic foundation from which eventually evolved. Then review general formulation, and look at finite sum setup. The last parts are devoted to various recent (not necessarily stochastic) advances in algorithms

We define an integral of real-valued functions with respect to a measure that takes its values in the extended positive cone partially ordered vector space $E$. The monotone convergence theorem, Fatou's lemma, and dominated theorem are established; analogues classical ${\mathcal L}^1$- ${\mathrm L}^1$-spaces investigated. results extend earlier work by Wright specialise those for Lebesgue when ...

The work of H. Hundal (Nonlinear Anal. 57 (2004), 35-61) has revealed that the sequence generated by the method of alternating projections converges weakly, but not strongly in general. This paper seeks to design strongly convergent algorithms by means of alternating the resolvents of two maximal monotone operators, A and B, that can be used to approximate common zeroes of A and B. In particula...