Sufficient Conditions
Sufficient conditions for a constrained local maximum or minimum can be stated in terms of a sequence of principal minors (determinants of upper-left-justified sub-matrices) of the bordered Hessian matrix of second derivatives of the Lagrangian expression.
Read more about this topic: Lagrange Multiplier
Famous quotes containing the words sufficient conditions, sufficient and/or conditions:
“We as a nation need to be reeducated about the necessary and sufficient conditions for making human beings human. We need to be reeducated not as parents—but as workers, neighbors, and friends; and as members of the organizations, committees, boards—and, especially, the informal networks that control our social institutions and thereby determine the conditions of life for our families and their children.”
—Urie Bronfenbrenner (b. 1917)
“It was not sufficient for the disquiet of our minds that we disputed at the end of seventeen hundred years upon the articles of our own religion, but we must likewise introduce into our quarrels those of the Chinese. This dispute, however, was not productive of any great disturbances, but it served more than any other to characterize that busy, contentious, and jarring spirit which prevails in our climates.”
—Voltaire [François Marie Arouet] (1694–1778)
“Armies, for the most part, are made up of men drawn from simple and peaceful lives. In time of war they suddenly find themselves living under conditions of violence, requiring new rules of conduct that are in direct contrast to the conditions they lived under as civilians. They learn to accept this to perform their duties as fighting men.”
—Gil Doud, U.S. screenwriter, and Jesse Hibbs. Walter Bedell Smith (Himself)