Simplex

Simplex is a term used in various fields of mathematics, particularly in geometry and optimization. In the context of geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. In the field of optimization, the simplex method is a popular algorithm for linear programming.

Geometry

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. For example, a 0-simplex is a point, a 1-simplex is a line segment, a 2-simplex is a triangle, a 3-simplex is a tetrahedron, a 4-simplex is a 5-cell and so on. The simplex is the simplest possible polytope in any given space.

Optimization

In the field of optimization, the simplex method is a popular algorithm for linear programming. The method is a systematic procedure for generating and examining candidate vertex solutions to a linear program. The simplex method can be viewed as a path-following algorithm in which the path is a sequence of edges of a polytope.

See also

• Linear programming
• Polytope
• Geometry

Simplex Resources
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