History of Projected Dynamical Systems
Projected dynamical systems have evolved out of the desire to dynamically model the behaviour of nonstatic solutions in equilibrium problems over some parameter, typically take to be time. This dynamics differs from that of ordinary differential equations in that solutions are still restricted to whatever constraint set the underlying equilibrium problem was working on, e.g. nonnegativity of investments in financial modeling, convex polyhedral sets in operations research, etc. One particularly important class of equilibrium problems which has aided in the rise of projected dynamical systems has been that of variational inequalities.
The formalization of projected dynamical systems began in the 1990s. However, similar concepts can be found in the mathematical literature which predate this, especially in connection with variational inequalities and differential inclusions.
Read more about this topic: Projected Dynamical System
Famous quotes containing the words history of, history, projected and/or systems:
“This is the greatest week in the history of the world since the Creation, because as a result of what happened in this week, the world is bigger, infinitely.”
—Richard M. Nixon (1913–1995)
“The history of the past is but one long struggle upward to equality.”
—Elizabeth Cady Stanton (1815–1902)
“Few white citizens are acquainted with blacks other than those projected by the media and the so—called educational system, which is nothing more than a system of rewards and punishments based upon one’s ability to pledge loyalty oaths to Anglo culture. The media and the “educational system” are the prime sources of racism in the United States.”
—Ishmael Reed (b. 1938)
“Before anything else, we need a new age of Enlightenment. Our present political systems must relinquish their claims on truth, justice and freedom and have to replace them with the search for truth, justice, freedom and reason.”
—Friedrich Dürrenmatt (1921–1990)