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pepitosbarzeguti@katamail science forum beginner
Joined: 22 Sep 2005
Posts: 3

Posted: Thu Jul 13, 2006 5:46 pm Post subject:
LP problem conversion



A need help for this LP problem (coming from kinematic theorem
structural analysis)
Ho to convert the problem:
T
minimize(Fc u)
subject to:
T
Fv u = 1
A u + N z = 0
z >= 0
Fc,Fv,u,z are vector's A and N are matrix.
to the standard LP format?
minimize( F=c0+c1 xm+1 .....+cn xm+n )
x1=a11 x[m+1] + ..............+ a1n x[m+n]
.......
xm=am1 x[m+1] + ..............+ amn x[m+n]
and bound variable's:
l1 <= x1 <= u1
.....
l(m+n) <= x[m+n] <= u(m+n)
Thank's in advance and sorry for the poor english 

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Peter Spellucci science forum Guru
Joined: 29 Apr 2005
Posts: 702

Posted: Fri Jul 14, 2006 2:10 pm Post subject:
Re: LP problem conversion



In article <1152812789.510709.110330@m73g2000cwd.googlegroups.com>,
"pepitosbarzeguti@katamail.com" <pepitosbarzeguti@katamail.com> writes:
Quote:  A need help for this LP problem (coming from kinematic theorem
structural analysis)
Ho to convert the problem:
T
minimize(Fc u)
subject to:
T
Fv u = 1
A u + N z = 0
z >= 0
Fc,Fv,u,z are vector's A and N are matrix.
to the standard LP format?
minimize( F=c0+c1 xm+1 .....+cn xm+n )
x1=a11 x[m+1] + ..............+ a1n x[m+n]
......
xm=am1 x[m+1] + ..............+ amn x[m+n]
and bound variable's:
l1 <= x1 <= u1
....
l(m+n) <= x[m+n] <= u(m+n)
Thank's in advance and sorry for the poor english

there is no need to transform the problem into this form and indeed your
explicit elimination occurs implicitly only in the simplex algorithm
LP software also does not require to have all variables bounded from below
or above.
you simply have
minimize c^T u + o*^T z = (c^T,o^T)*(u;z)
subject to
[ Fv^T o^T ] [ u ] = [1]
[ A N ] [ z ] [0]
z>=0
unknowns x=[u;z]
only part of the unknowns restricted to be positive
matrix composed from a row Fv^T o^T and the matrix block row A N
and z not appearing in the objective. this is already a rather standard LP
and could be solved by any reasonable LP solver
hth
peter 

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