I first studied linear programming in the mid-70's, and the course textbook was by David Gale (originally out in 1960). Using Google Books, I was able to dig it up
- he uses canonical form for the equality constraint version:
Look on Page 75.
Another textbook popular at that time was by Saul Gass (1958) who uses standard form for the equality constraint version:
Look on page 129.
Bob Vanderbei, a ex-colleague (but still a friend) of mine from Bell Labs, now a professor at Princeton, uses standard form to apply to the inequality version in his book
(first edition from 1996):
Look on page 57
A book by Dantzig and Thapa uses standard form to apply to equality constraint version:
See page 48
A more recent book by Karloff (2009) uses standard form to apply to equality and canonical form to apply to the inequality case.
Look at page 5
So, just based on my not-so random sample, I have to go with Andrew's terminology (that the Standard Form applies to the equality version) since it seems like that is used a little more than the others. Breaks
my heart to do so :)
Sent: Thursday, May 12, 2011 1:21 PM
To: Meketon, Marc
Cc: Robbie Morrison; GLPK help
Subject: Re: [Help-glpk] optimality conditions paragraph (KKT and LP formulations)
> > Many books call the min c'x, s.t. Ax=b, x>=0 form the "canonical"
> > linear programming program. The min c'x s.t. Ax >= b, x>=0 is
> > often called the "standard" form, because it has more symmetry with
> > the dual (which is max b'y s.t. A'y<=c, y>=0).
I consulted the "Encyclopedia on Optimization" by Floudas and Pardalos (Eds.), Springer, 2009. The article "Linear Programming" by P.Pardalos, pp.1883-1886, Section "Problem Description", says:
"Consider the linear programming problem (in standard form):
s.t. Ax = b
x >= 0
The same term "standard form" is used in the next article "Linear
Programming: Interior Point Methods" by K.M.Anstreicher, and some other articles dedicated to linear programming.
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