Donna
[EMAIL PROTECTED]
On 29-Jun-06, at 12:29 PM, John Randall wrote:
If you are interested in linear programming (I'm not sure if you
are, or
whether you were just citing an example), you might want to take a
look at
I think it is clear what I am interested in.
http://www.jsoftware.com/jwiki/Stories/RichardBrown
which contains an annotated description of using the simplex
algorithm in J.
Too bad I did not have the time yet to read the entire wiki else I
could have saved myself the trouble of trying to explain many things
you alredy knew of and have found a lexicon with which you seem more
comfortable as well as the J expressions I am not yet able to produce
quickly enough to include in a reply
so in summary
Dr Brown discusses the simplex method.
On 28-Jun-06, at 2:24 PM, dly wrote:
Unlike the case for general LP problems which are almost
universally solved by one algorithm
By the magic of modern mathematics it can be shown that the one
algorithm referred to by dly is the simplex method discussed by Dr Brown
Dr Brown says:
However, there is a catch: if the denominator is zero or negative
then the constraint should be ignored.
On 28-Jun-06, at 2:24 PM, dly wrote:
there are (were?) large numbers of Integer LP algorithms none of
which were universally successful in solving LARGE problems. The
primary limitation is the number of integer variables so if there
are more than few hundred variables they cannot be solved except in
special cases.
Anyway, some methods to approach such problems involve building a
simplex plateau as for general problems but with only integer
elements and this property must be maintained at each iteration.
INTEGER not RATIONAL, but if you are forced at some step to say
divide 111 by 333 you might want to keep the result as 111r333 and
go on until a later step where you can get back into an Integer.
You are best to consult the literature as this is getting quite
long and I don't seem to be making it clear.
For INTEGER LP problems there is one other catch 22 because you don't
just have to keep it real or try to be positive you have to keep it
wholesome
And wouldn't it be nice if there were a convenient notation which
would help you do this when the result did not turn out to be an
integer such as 1r3 and wouldn't it be like dreaming in colour if
better than this it could tell you it was actually 111r333 because
that would be the cat's meow
QED
More generally, you will probably learn more from trying a solve a
familiar problem in J than from any amount of discussion here.
Au contraire.
Who would have thought that 18 years after the fact I would get to
continue my discussion with Dr Brown--I am elated. (Of course,
subject to debate and I might also be wrong because you see I'm no
expert.
Thank you very very much!
Donna
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