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## Re: Linear Programing

 From: Etienne Grossmann Subject: Re: Linear Programing Date: Fri, 24 Nov 2000 08:05:19 +0000 User-agent: WEMI/1.13.7 (Shimada) FLIM/1.13.2 (Kasanui) Emacs/20.7 (i386-debian-linux-gnu) (with unibyte mode)

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Hello,

Jeff's program does

max f'*x     subject to   A*x == b and x >= 0
x

And you want :

LP     Linear programming.
X=LP(f,A,b) solves the linear programming problem:

min f'x    subject to:   Ax <= b
x

I think you can transform your problem into a problem that Jeff's
program can solve. The reasoning (no warranty of correctness : I would
not at all be surprised if there were some pitfall I fell in) is :

Your problem is equivalent to (set y = A*x - b, y should be >= 0)

max f'*x         subject to   A*x - y == b and x >= 0 and y>=0
x

which is equiv. to            (rewrite in vectorial form)

max [f',0]*[x;y] subject to   [A,-eye]*[x;y] == b and [x;y]>=0
x

equiv. to
(set x = x1 - x2 with x1 >= 0 and x2 >= 0, idem for y = y1 - y2)

max [f',-f',0,0]*[x1;x2;y1;y2]
x

subject to   [A,-A,-eye,-eye]*[x1;x2;y1;y2] == b
and          [x1;x2;y1;y2]>=0

Which is the kind of problem that Jeff's function solves.

Etienne

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