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A point in a convex set that cannot be expressed as a convex combination of two other distinct points in the set. Extreme points are also known as corner points or vertices. The extreme points of a rectangle are its four vertices, while the extreme points of a circular disc are the points on its circumference. For a linear programming problem, the extreme points of its convex set of solutions correspond to basic feasible solutions, and it can be shown that, if the problem has a finite optimal solution, then one of the extreme points is optimal.