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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).
One example is the design of optimal tax instruments. The tax instrument is modeled in the upper level and the clearing market is modeled in the lower level. In general, the lower level problem may be an optimization problem or a variational inequality. Several keywords are provided to facilitate reformulating hierarchical optimization problems.
Mathematical programming with equilibrium constraints (MPEC) is the study of constrained optimization problems where the constraints include variational inequalities or complementarities. MPEC is related to the Stackelberg game. MPEC is used in the study of engineering design, economic equilibrium, and multilevel games.
(There are examples showing that attractivity does not imply asymptotic stability. [ 9 ] [ 10 ] [ 11 ] Such examples are easy to create using homoclinic connections .) If the Jacobian of the dynamical system at an equilibrium happens to be a stability matrix (i.e., if the real part of each eigenvalue is strictly negative), then the equilibrium ...
One of the simplest examples of such a system is the case of a bathtub with the tap open but without the bottom plug: [dubious – discuss] after a certain time the water flows in and out at the same rate, so the water level (the state variable being Volume) stabilizes and the system is at steady state. Of course the Volume stabilizing inside ...
A contact equilibrium may be regarded also as an exchange equilibrium. There is a zero balance of rate of transfer of some quantity between the two systems in contact equilibrium. For example, for a wall permeable only to heat, the rates of diffusion of internal energy as heat between the two systems are equal and opposite.
In thermodynamics, a quasi-static process, also known as a quasi-equilibrium process (from Latin quasi, meaning ‘as if’ [1]), is a thermodynamic process that happens slowly enough for the system to remain in internal physical (but not necessarily chemical) thermodynamic equilibrium. An example of this is quasi-static expansion of a mixture ...
A well-known example of the minority game is the El Farol Bar problem proposed by W. Brian Arthur. A hybrid form of coordination and anti-coordination is the discoordination game , where one player's incentive is to coordinate while the other player tries to avoid this.