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  "body": "\n## Summary\n\nThe simplex algorithm, introduced by George Dantzig, solves [[linear programs|VNMXB0J2KA]].\nIt walks from vertex to adjacent vertex of the feasible polyhedron along edges, never decreasing the objective, until no neighbouring vertex is better.\nIn practice it is fast.\nBut for the usual pivot rules there are inputs, such as the Klee–Minty cubes, on which it takes exponentially many steps.\nThe question of how few steps suffice in the worst case is linked to the diameter of polytope graphs and to the [[Hirsch conjecture|ZBVJ4B41AX]].\n\n## Explanations\n\n### L1 human\n\nPicture the allowed region of a linear program as a many-sided gem, and the objective as height.\nStart at one corner, look at the edges going up, and walk along one of them to the next corner.\nRepeat until every edge at the current corner goes down; that corner is the highest point of the gem.\nBecause the gem is convex, a corner with no upward edge is the top.\n",
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