Lesson plan
Basic solution (linear programming)
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 P and a vector \mathbf{x}^* \in \mathbb{R}^n , \mathbf{x}^* is a basic solution if: # All the equality constraints defining P are active at \mathbf{x}^* # Of all the constraints that are active at that vector, at least n of them must be linearly independent. Note that this also means that at least n constraints must be active at that vector. A constraint is active for a particular solution \mathbf{x} if it is satisfied at equality for that solution. A basic solution that satisfies all the constraints defining P (or, in other words, one that lies within P ) is called a basic feasible solution.
Article summary
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 P and a vector \mathbf{x}^* \in \mathbb{R}^n , \mathbf{x}^* is a basic solution if: # All the equality constraints defining P are active at \mathbf{x}^* # Of all the constraints that are active at that vector, at least n of them must be linearly independent. Note that this also means that at least n constraints must be active at that vector. A constraint is active for a particular solution \mathbf{x} if it is satisfied at equality for that solution. A basic solution that satisfies all the constraints defining P (or, in other words, one that lies within P ) is called a basic feasible solution.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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