extreme point

extreme point (plural extreme points)

1. (mathematics) A point in a convex set which does not lie in any open line segment joining two points in the set.
   • 1970, R. Tyrrell Rockafellar -, Convex Analysis, →ISBN, page 162:

     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.

2. (mathematics) The maximum or minimum of a function.
   • 2001, Encyclopedia of Optimization, →ISBN, page 288:

     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.

3. (mathematics) A leaf vertex of a tree data structure.
   • 2004, Antonio Laganà, Marina L. Gavrilova, Vipin Kumar, Computational Science and Its Applications, →ISBN:

     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 testing the inclusion of the extreme point in the interval.

4. A point that is physically located farthest in the direction of the edge of something.
   • 2002, Micheal Jacq-Hergoualc'h, The Malay Peninsula: Crossroads of the Maritime Silk-Road (100 BC - 1399 AD), →ISBN:

     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 alluvial deposits along the coasts has already been mentioned.

   • 2015, Clements R. Markham, A Memoir on the Indian Surveys, →ISBN, page 10:

     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, Thomas Wright, A Monograph on the British Fossil Echinodermata of the Oolitic Formations, →ISBN, page 15:

     With a pair of scissors I then lay open the upper surface of all the rays by a straight incision down the middle, from the circumfrance of the anal circle to the extreme point of the ray, and, folding down the two flaps thus produced from each adjoining rays together; when the whole of the flaps are thus united, I raise the border of the flat disc and form the whole into a globular shape, taking care to make the extreme points of the rays, with their eye-spots, touch the margin of the anal circle, which must be elevated likewise to a sufficient height, by cutting across the sand canal and other adhesions to meet the ends of the rays, and thereby form a globe.

5. A standpoint that goes farthest in some dimension or on some criterion.
   • 2007, James H. Husted, Gladys Husted, Ethical Decision Making in Nursing and Health Care, →ISBN, page 267:

     Any claim that they violate her right to freedom in not applying heroic measures is one of the extreme points of ethical absurdity.

   • 2014, Carlos H. Waisman, Modernization and the Working Class: The Politics of Legitimacy, →ISBN:

     Their extreme points will be called consent-dissent, in relation to beliefs, and compliance-radicalism, in relation to behavior.

   • 2014, John Roberts, Photography and Its Violations, →ISBN, page 21:

     This is why photography needs to mediate its critical possibilities and limitations not just through a state-of-exception—or its cousin, the atrocity image—even if these things represent the extreme points of the social ontology of photography in the current period and should be defended as evidence of systemic crisis.