simplex method
An algorithm that walks from vertex to vertex of an LP's feasible region, always improving the objective.
The simplex method solves a linear program by moving between adjacent vertices (basic feasible solutions) of the feasible polyhedron, at each step pivoting to a neighboring vertex with an equal or better objective value, until no adjacent vertex improves further — at which point the current vertex is optimal (per the extreme point theorem, an optimum always exists at some vertex).
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