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The first problem involving a variational inequality was the Signorini problem, posed by Antonio Signorini in 1959 and solved by Gaetano Fichera in 1963, according to the references (Antman 1983, pp. 282–284) and (Fichera 1995): the first papers of the theory were (Fichera 1963) and (Fichera 1964a), (Fichera 1964b).
The obstacle problem is a classic motivating example in the mathematical study of variational inequalities and free boundary problems.The problem is to find the equilibrium position of an elastic membrane whose boundary is held fixed, and which is constrained to lie above a given obstacle.
Since then the study of complementarity problems and variational inequalities has expanded enormously. Areas of mathematics and science that contributed to the development of complementarity theory include: optimization, equilibrium problems, variational inequality theory, fixed point theory, topological degree theory and nonlinear analysis.
In mathematics, a differential variational inequality (DVI) is a dynamical system that incorporates ordinary differential equations and variational inequalities or complementarity problems. DVIs are useful for representing models involving both dynamics and inequality constraints.
Finite-Dimensional Variational Inequalities and Complementarity Problems, Volume I This page was last edited on 27 January 2022, at 06:45 (UTC). Text ...
Many free boundary problems can profitably be viewed as variational inequalities for the sake of analysis. To illustrate this point, we first turn to the minimization of a function F {\displaystyle F} of n {\displaystyle n} real variables over a convex set C {\displaystyle C} ; the minimizer x {\displaystyle x} is characterized by the condition
The Huffington Post collaborated with The Hechinger Report, a nonprofit, independent news organization focused on inequality and innovation in education, to produce this story as part of a series on the impact of police in schools. Rebecca Klein is a reporter and editor who covers education for The Huffington Post.
Differential inclusions arise in many situations including differential variational inequalities, projected dynamical systems, Moreau's sweeping process, linear and nonlinear complementarity dynamical systems, discontinuous ordinary differential equations, switching dynamical systems, and fuzzy set arithmetic. [1]