In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all the value of a given variable, belonging usually to a convex set. The mathematical theory of variational inequalities was initially developed to deal with equilibrium problems, precisely the Signorini problem: in that model problem, the functional involved was obtained as the first variation of the involved potential energy therefore it has a variational origin, recalled by the name of the general abstract problem. The applicability of the theory has since been expanded to include problems from economics, finance, optimization and game theory.
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Famous quotes containing the word inequality:
“All the aspects of this desert are beautiful, whether you behold it in fair weather or foul, or when the sun is just breaking out after a storm, and shining on its moist surface in the distance, it is so white, and pure, and level, and each slight inequality and track is so distinctly revealed; and when your eyes slide off this, they fall on the ocean.”
—Henry David Thoreau (1817–1862)