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!
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
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!