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Some numerical algorithms for elliptic eigenvalue problems are proposed, analyzed, and numerically tested. The methods combine advantages of the two-grid algorithm, two-space method, the shifted inverse power method, and the polynomial…
This paper proposes an extra gradient Anderson-accelerated algorithm for solving pseudomonotone variational inequalities, which uses the extra gradient scheme with line search to guarantee the global convergence and Anderson acceleration to…
Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the maximum entropy principle and leads to thermodynamically…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
The aim of this paper is to prove the existence of periodic solutions to symmetric Newtonian systems in any neighborhood of an isolated orbit of equilibria. Applying equivariant bifurcation techniques we obtain a generalization of the…
In this paper we present the bilevel equilibrium problem under conditions of pseudomonotonicity. Using Bregman distances on Hadamard manifolds we propose a framework for to analyse the convergence of a proximal point algorithm to solve this…
This paper presents a modified iterative approach to solve the variational inequality problem using the double inertial technique in the context of a real Hilbert space. Our iterative technique involves a projection onto a generalized…
We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
In this paper we study the fundamental problems of maximizing a continuous non-monotone submodular function over the hypercube, both with and without coordinate-wise concavity. This family of optimization problems has several applications…
In this paper, we introduce an iterative process which converges strongly to a common element of sets of solutions of finite family of generalized equilibrium problems, sets of fixed points of finite family of continuous relatively…
In this paper, using sunny generalized nonexpansive retraction, we propose new extragradient and linesearch algorithms for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a…
Monotone inclusions have a wide range of applications, including minimization, saddle-point, and equilibria problems. We introduce new stochastic algorithms, with or without variance reduction, to estimate a root of the expectation of…
We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coefficients, integral representations of solutions, a numerical…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
In this paper, we study a class of generalized monotone variational inequality (GMVI) problems whose operators are not necessarily monotone (e.g., pseudo-monotone). We present non-Euclidean extragradient (N-EG) methods for computing…
We establish the existence of weak solutions of coupled systems of elliptic partial differential equations with quasimonotone nonlinearities in the domain interior and on the boundary. When the nonlinearities satisfy some monotonicity…
In this work, we introduce the notion of regularization of bifunctions in a similar way as the well- known convex, quasiconvex and lower semicontinuous regularizations due to Crouzeix. We show that the Equilibrium Problems associated to…
In this paper, we introduce two novel parallel projection methods for finding a solution of a system of variational inequalities which is also a common fixed point of a family of (asymptotically) $\kappa$ - strict pseudocontractive…