Optimization problems

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In mathematics, computer science and economics,
an optimization problem is the problem of finding the best solution
from all feasible solutions.

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In the theory of linear programming,
a basic feasible solution (BFS) is a solution with a minimal set of non-zero variables.

Geometrically, each BFS corresponds to a corner of the polyhedron of feasible solutions.

If there exists an optimal solution, then there exists an optimal BFS.
Hence, to find an optimal solution, it is sufficient to consider the BFS-s.

This fact is used by the simplex algorithm,
which essentially travels from some BFS to another until an optimal one is found.[1]