checking for linear independence inside an optimization problem

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ipandro@gmail.com - 18 Apr 2006 03:23 GMT

The solution of my optimization problem is a matrix (i.e., n vectors).
However, the solution I am looking for should be such that the n
vectors are linearly independent. Therefore, I am trying to model the
linear independence check as a set of constraints. Thus far, I have
only be able to model this through the Cholesky decomposition of the
original matrix which introduces two sets of bilinear equality
contraints thus making my problem very difficult.
Any suggestions as to other possible reformulations?
Thank you,
Yannis

ipandro@gmail.com

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Peter Spellucci - 19 Apr 2006 11:42 GMT

>The solution of my optimization problem is a matrix (i.e., n vectors).
>However, the solution I am looking for should be such that the n
[quoted text clipped - 8 lines]
>
>ipandro@gmail.com

if your matrix allows a cholesky decomposition, then, rather than
adding this as a constraint you could take the components of the
cholesky factor as the original variables (which makes your
functions more involved but completely rmeove these nonlinear
equality constriants which always are hard to handle
hth
peter

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Math Forum / Mathematics / Operations Research / April 2006

checking for linear independence inside an optimization problem