extreme point

Noun

extreme point (plural extreme points)

1. A point in a convex set which does not lie in any open line segment joining two points in the set.
   • For convex cones, the concept of an extreme point is not of much use, since the origin would be the only candidate for an extreme point.1970, R. Tyrrell Rockafellar -, Convex Analysis, →ISBN, page 162
2. The maximum or minimum of a function.
   • At first glance, degeneracy, a concept based on properties of extreme point solutions, does not seem to be as serious a problem for IPMs as it is for simplex methods.2001, Encyclopedia of Optimization, →ISBN, page 288
3. A leaf vertex of a tree data structure.
   • Since the extreme points are sorted in an ascending order, and it is known that there is no more event other than the event at the current leftmost extreme point, and therefore we traverse from the root of the tree to the bottom while we re-evaluating the new interval values of each node and...2004, Antonio Laganà, Marina L. Gavrilova, Vipin Kumar, Computational Science and Its Applications, →ISBN
4. A point that is physically located farthest in the direction of the edge of something.
   • This is not the case, however, because it is protected from the summer monsoon in the southwest by the Island of Sumatra, and from the winter monsoon in the northeast by the overhang of the peninsula of Cà Mau, the extreme point of the Indochinese Peninsula, a set of circumstances whose effect on...2002, Michel Jacq-Hergoualc'h, translated by Victoria Hobson, The Malay Peninsula: Crossroads of the Maritime Silk-Road (100 BC - 1300 AD), →ISBN
   • He measured bases on shore by running a ten-foot rod along a cord stretched tight between the extreme points, and kept in position by stakes, the direction being verified by a telescope.2015, Clements R. Markham, A Memoir on the Indian Surveys, →ISBN, page 10
5. A standpoint that goes farthest in some dimension or on some criterion.
   • Any claim that they violate her right to freedom in not applying heroic measures is one of the extreme points of ethical absurdity.2007, James H. Husted, Gladys Husted, Ethical Decision Making in Nursing and Health Care, →ISBN, page 267
   • Their extreme points will be called consent-dissent, in relation to beliefs, and compliance-radicalism, in relation to behavior.2014, Carlos H. Waisman, Modernization and the Working Class: The Politics of Legitimacy, →ISBN