In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values 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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In mathematics, a variationalinequality is an inequality involving a functional, which has to be solved for all possible values of a given variable,...
differential variationalinequality (DVI) is a dynamical system that incorporates ordinary differential equations and variationalinequalities or complementarity...
Y = (2, 0) are not. A complementarity problem is a special case of a variationalinequality. Complementarity problems were originally studied because the Karush–Kuhn–Tucker...
conditions can also be written is a more compact form (the integro-variationalinequality): max { A ϕ + L , M − ϕ } = 0 {\displaystyle \max \left\{{\mathcal...
problem is a classic motivating example in the mathematical study of variationalinequalities and free boundary problems. The problem is to find the equilibrium...
The proof that continuous finite variation processes have zero quadratic variation follows from the following inequality. Here, P {\displaystyle P} is a...
Social inequality occurs when resources within a society are distributed unevenly, often as a result of inequitable allocation practices that create distinct...
In variational Bayesian methods, the evidence lower bound (often abbreviated ELBO, also sometimes called the variational lower bound or negative variational...
Sciences (INFORMS), in recognition of her lifetime achievement in "variationalinequalities, the price of anarchy, dynamic pricing and data analytics," and...
aided in the rise of projected dynamical systems has been that of variationalinequalities. The formalization of projected dynamical systems began in the...
convex set. Many free boundary problems can profitably be viewed as variationalinequalities for the sake of analysis. To illustrate this point, we first turn...
many kinds of inequalities involving matrices and linear operators on Hilbert spaces. This article covers some important operator inequalities connected with...
x_{i}=u_{i},\;F_{i}(x)\leq 0} . Another definition for MCP is: it is a variationalinequality on the parallelepiped [ ℓ , u ] {\displaystyle [\ell ,u]} . Complementarity...
the Signorini problem coincides with the birth of the field of variationalinequalities. The content of this section and the following subsections follows...
Wealth disparity in major cities Economic inequality is an umbrella term for a) income inequality or distribution of income (how the total sum of money...
sometimes called the statistical distance, statistical difference or variational distance. Consider a measurable space ( Ω , F ) {\displaystyle (\Omega...
Attention inequality is the inequality of distribution of attention across users on social networks, people in general, and for scientific papers. Yun...
Gender inequality is the social phenomenon in which people are not treated equally on the basis of gender. This inequality can be caused by gender discrimination...
Institute of Technology, with the dissertation Solving Asymmetric VariationalInequality Problems and Systems of Equations with Generalized Nonlinear Programming...
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