Bland's rule

With Bland's rule, the simplex algorithm solves feasible linear optimization problems without cycling.

However, there are examples of degenerate linear programs, on which the original simplex algorithm cycles forever.

Assuming that the problem is to minimize the objective function, the algorithm is loosely defined as follows: It can be formally proven that, with Bland's selection rule, the simplex algorithm never cycles, so it is guaranteed to terminate in a bounded time.

While Bland's pivot rule is theoretically important, from a practical perspective it is quite inefficient and takes a long time to converge.

[4]: 72–76 In the abstract setting of oriented matroids, Bland's rule cycles on some examples.