Abstract
Variational inequality and complementarity have much in common, but there has been little direct contact between the researchers of these two related fields ofmathematical sciences. Several problems arising from fluid mechanics, solid mechanics, structural engineering, mathematical physics, geometry, mathematical programming, and so on have the formulation of a variational inequality or complementarity problem. People working in applied mathematics mostly deal with the infinitedimensional case and they deal with variational inequality whereas people working in operations research mostly deal with the finite-dimensional problem and they use the complementarity problem. Variational inequality is a formulation for solving the problem where we have to optimize a functional. The theory is derived by using the techniques of nonlinear functional analysis such as fixed point theory and the theory of monotone operators, among others.
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