NMath User's Guide

Chapter 27. Linear Programming (.NET, C#, CSharp, Visual Basic, VB.NET)

In NMath, class SimplexLPSolver solves linear programming problems using the simplex method. A linear programming (LP) problem optimizes a linear objective function subject to a set of linear constraints, and optionally subject to a set of variable bounds. For example:

Maximize
Z = X1 + 4 X2 + 9 X3

Subject To
X1 + X2 <= 5
X1 + X3 >= 10
-X2 + X3 = 7

Bounds
0 <= X1 <= 4
0 <= X2 <= 1

The simplex method solves LP problems by constructing an initial solution at a vertex of a simplex, then walking along edges of the simplex to vertices with successively higher values of the objective function until the optimum is reached.

This chapter describes how to use class SimplexLPSolver.

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