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Little Green Book

APPENDIX 1: PROPERTIES OF LINEAR PROGRAMMING PROBLEMS

Suppose that any two points, 1 and 2 , are chosen from a closed region R. If these points are connected by a straight line segment and all of the points lying on this straight line segment are also contained in R, then the collection of points is called a convex set – that is, let 1 , 1 be any two points contained in a closed region R. If all points , where lie within R for all 1 and 2 , then the collection of points within R is a convex set. If a point of a convex set cannot be expressed as a linear combination of two other points from the convex set as in equation 1, then such a point is called an extreme point. Example : Vertices of polygons are extreme points. A point that is a combination of points 1 , 2 , …, ...

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