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# Simplicial Pivoting Algorithms for Integer Programming

### Article Outline

Keywords

Keywords Simplicial algorithms - Integer programming - Knapsack problem - Horn formulas

Simplicial *path following methods* are relatively new in the area of integer programming (cf. Integer programming). They are based on a *triangulation* of Euclidean space and a *pivoting algorithm* which, for a restrictive class of problems, terminates with an integral solution or shows that no such solution exists. The path constructed consists of a sequence of neighboring *simplices* , the vertices of which are integral lattice points.

Simplicial methods originated in *fixed point theory* , where they are used to approximate fixed points of continuous mappings [7,18].

In the area of continuous mathematics they have been applied successfully