Английская Википедия:Basic solution (linear programming)

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In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions.

For a polyhedron <math>P</math> and a vector <math> \mathbf{x}^* \in \mathbb{R}^n</math>, <math>\mathbf{x}^*</math> is a basic solution if:

1. All the equality constraints defining <math>P</math> are active at <math>\mathbf{x}^*</math>
2. Of all the constraints that are active at that vector, at least <math>n</math> of them must be linearly independent. Note that this also means that at least <math>n</math> constraints must be active at that vector.

A constraint is active for a particular solution <math>\mathbf{x}</math> if it is satisfied at equality for that solution.

A basic solution that satisfies all the constraints defining <math>P</math> (or, in other words, one that lies within <math>P</math>) is called a basic feasible solution.

References

Шаблон:Mathapplied-stub