Assume that A is a bounded self-adjoint operator in a Hilbert space H. Then, the variational principle max v |(Au, v)|2 (Av, v) = (Au, u) (*) holds if and only if A ≥ 0, that is, if (Av, v) ≥ 0 for all v ∈ H. We define the quotient on the left-hand side in (*) to be zero if (Av, v) = 0. As an application of this principle a variational principle for the electrical capacitance of a conductor of ...

In this paper, we suggest and analyze some three-step iterativemethods for solving general nonconvex variational inequalities using the technique of updating the solution. We show that the convergence of these iterativemethods requires only the partially relaxed strongly monotonicity which is a weaker condition than cocoerciveness.We are also discuss several special cases. Our method of proof i...

Variational inequalities represent very useful and powerful tools for investigation and solution of many equilibrium type problems arising in Economics, Engineering, Operations Research and Mathematical Physics. The talk is devoted to several rather new approaches from [1]–[5] to construction of solution methods for variational inequalities with multi-valued cost mappings. We recall that the pr...

1 Department of Mathematics, Nanjing University, Nanjing 210093, China 2 Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA 3 Mathematics Department, COMSATS Institute of Information Technology, Islamabad, Pakistan 4 Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan 5 School of Mathematics and LPMC, Nankai University, Tianjin...

In this paper, we introduce and study the system of general variational inequalities which is equivalent to the general variational inequality problem over the product of sets. The usual concept of monotonicity has been extended here. We establish existence results for the solution of general variational inequality problem over the product of sets in the setting of real Hausdroff topological ve...

In this article, we prove the existence of nontrivial weak solutions for a class of discrete boundary value problems. The main tools used here are the variational principle and critical point theory.

In this paper, we introduce and consider a new class of equilibrium variational inequalities, called the mixed general equilibrium bifunction variational inequalities. We suggest and analyze some proximalmethods for solvingmixed general equilibriumbifunction variational inequalities using the auxiliary principle technique. Convergence of these methods is considered under somemild suitable condi...

In this paper, we introduce a general iterative scheme for finding a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of solutions of variational inequalities for an inverse-strongly monotone mapping.