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Re:Google Optimization Tools by graycat on Wednesday July 08, 2015 @08:11AM (#9851031)
Yup!

IMHO it has been, since the 1950s, mostly this "sprinting" that was in practice just too difficult, that is, too costly in time and money, for far too large a fraction of organizations, budgets, managers, etc. that could have used optimization.

Now with current computing and the Internet, a lot in applied math, in principal powerful and valuable for important real problems, seems to be growing significantly in popularity. The "sprinting" is much easier but, sadly, too often still too challenging.

Of course part of the "sprinting" challenge was solved by, say, A Mathematical Programming Language (AMPL) where can just type in something like

        max z = f(x)
     subject to g(x) >= 0
                  x in C 
where for large positive integers m and n and the real numbers R, x in R^m and g: R^m --> R^n.

So, then, with the problem thusly typed in, just need a solver! Right: Maybe from the back side of one of the moons of Pluto?

Gee, we know how to sort, know a lot about sorting, in O( n log(n) ), etc., so maybe we should have solvers that would do as well on optimization as we can do now on sorting? Then quickly we encounter the monster of the question P versus NP.

So, without an algorithm that shows that P = NP, we're back to column generation here, Lagrangian relaxation there, branch and bound too often, some group theory sometimes, etc. and "sprinting".

Yes, it was interesting philosophically how central and challenging P versus NP is, but I'd rather have just had a way to solve optimization problems routinely, gotten home in time for dinner, and spent Sunday at a BBQ!

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