A form of Klee-Minty formally proven?
Dear all:
Is there a source (book/script/...) which gives a complete and fully
formal proof that the simplex algorithm (in its max-form) with Dantzig's
rule requires 2^n different tableaux on the following Klee-Minty-kind
example:
maximize $\sum_{i=1}^n 2^{n-i}x_i$
subject to for all $i\in\{1,...,n\}$:
$\sum_{j=1}^{i-1} 2^{i-j+1}x_j + x_i \le 5^i$
?
All sources I found just treat other examples and/or leave the key proof
details to the reader.
One way would be to create a very explicit mapping from an index k to
the k-th tableau (k=1,...,2^n) in the execution of Dantzig's algorithm
on the above example.
Best,
Axel.
Fnews-brouse 1.9(20180406) -- by Mizuno, MWE <mwe@ccsf.jp>
GnuPG Key ID = ECC8A735
GnuPG Key fingerprint = 9BE6 B9E9 55A5 A499 CD51 946E 9BDC 7870 ECC8 A735