Being rusty and went to my bookshelf for a relevant text which is
circa 1974 and will give you an idea of how rusty my math may be.
I did not have the chance to use IBM's vector processor but it was
first described to me over lunch by Dr James Brown of IBM in 1988 I
believe on the occasion of a presentation of a new version of APL2.
(I might add that my IBM rep had simply introduced him as Jim Brown
and I had no idea of his role in APL2 until the presentation that
followed). He provided several illustrations of how APL2 was able to
take immediate advantage of the vector processor--which I envision as
a very special math coprocessor for the mainframe aimed at speeding
computation by performing calculations in parallel that had
previously been done seriatim due to Von Newman architecture. The APL
language, expressing everything in arrays that could be raveled to
vectors, could take immediate advantage of this.
He then mentioned an application that seemed to me to require an
Integer Linear Programming algorithm but did not mention having made
any special provision for this and when I questioned him on this
point he seemed confused and I realized that he was discussing an
application of one of his customers and early adopters of the IBM
Vector processor and was unfamiliar with what constraints their
actual application might require. Our lunch needed to be adjourned
because it was time for the presentation to begin. I was too
embarrassed, on learning who I had been debating with to pursue my
questioning after the proceedings.
In the text it states that no algorithm (i.e. in 1974) has shown
itself to consistently solve large integer programming problems.
In general linear programming models the results can assume any
values in the feasible region and are allowed to be continuous.
Altho for some problems such as transportation assignment or network
flow, integer solutions can be obtained automatically, the extreme
points of a general linear programming problem is not ordinarily
restricted to having only integer-valued components. Moreover one
cannot merely round the fractional values of an optimal solution and
expect it to produce the optimal value solution. In a mixed integer-
continuous variable problem only some of the variables are required
to be integers.
At the time (1974), there were three classes of algorithms (1)
cutting plane, (2) enumeration and (3) partitioning used as
additional constraints to ensure the solution or feasible region has
the desired integer properties. I was thus interested in 1988 and
again interested today in 2006 if there has been progress.
This is the reason I want to clearly understand limits and
constraints of any algorithms underlying any primitives of J.
Donna
[EMAIL PROTECTED]
On 27-Jun-06, at 4:42 PM, John Randall wrote:
Donna L.Y. wrote:
This information is extremely relevant to an integer Linear
Programming model a point apparently lost on some early users of
IBM's vector processor.
Donna:
Could you explain this a little? I know something about mixed and
pure
integer linear programming, but nothing about IBM's vector processor.
Thanks,
John
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