Multi-precision linear programming

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Michal Kvasnicka on 9 May 2020
Edited: Michal Kvasnicka on 12 May 2020
I need to solve specific linear programming problem which is based on Mallows permutation probability distribution. This exponential distribution for high distances of permutations suffer from the lose of accuracy. So, I need the multi-precision support to handle numerical consistency and stability of my linear programming problem.
What are my options with Matlab 2020a?

Michal Kvasnicka on 12 May 2020
Edited: Michal Kvasnicka on 12 May 2020
One of possible way (so far only known to me) how to solve directly and eficiently LP problems with full multi-precision support in MATLAB environment is using of Matlab toolbox for Maple (MTM) by built-in Maple function LPsolve (Optimization package) and multi-precision setup by Maple command "Digits:= 200", for example.
It would be great if the developers of Symbolic Math Toolbox could add in the future some optimization methods!

John D'Errico on 9 May 2020
Edited: John D'Errico on 9 May 2020
None in MATLAB. However, I there is some question as to you really need super high multiple precision support. Do you have data that is accurate to 20 or more digits of precision? If so, then I am impressed. And if your data is not that accurate, then the answers you would get from that extra high precision are just an illusion. But do as you will.
I might knote that few physical constants are known to that high precision. From what I can see, constants like the Planck constant, the Volt and the kilogram all seem to be accurate only to some parts per billion. If so, I'd be pretty impressed if you have information that is known to twice as many significant digits. Well done there.
Stephen on 12 May 2020
"I'd be pretty impressed if you have information that is known to twice as many significant digits"
MAD magazine issue 26 is known to be exactly one potrzebie thick, or 2.2633484517438173216473 mm.
I guess that makes MAD magazine a more fundamental unit than those so called "constants".

R2020a

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