[Trilinos-Users] Basis pursuit denoise (BPDN)

[Day, David]

Dear Einar,
    The Basis Pursuit problem is new to me.  This type of l1 minimization problem
is a special, relatively nice, linear programing problem.  I think that the inequality constraint is
typically an equality constraint.  I thought a little about the l2 relaxation problem.  But even this,
for general parameter values, has a solution that is sensitive to the near null space of A.   For some
parameters,  A,b,sigma,  you might try to solve the l2 relaxation, min norm(x,2), using one of the optimization packages in Trilinos, such as MOOCHO.

For linear programing, you might consider packages unrelated to Trilinos such as
glpk (gnu),  clp (COIR-OR repository), or cplex (which is now free to acaemics.

Yours faithfully,
David Day
________________________________
From: trilinos-users-bounces at software.sandia.gov [trilinos-users-bounces at software.sandia.gov] on behalf of einaro at yahoo.com [einaro at yahoo.com]
Sent: Friday, March 25, 2011 1:54 AM
To: trilinos-users at software.sandia.gov
Subject: [Trilinos-Users] Basis pursuit denoise (BPDN)

Dear experts,
I'd like to solve a Basis Pursuit denoise problem like

minimize ||x||_1  subject to  ||Ax - b||_2 <= sigma,

and I was hoping to use Trilinos for this purpose. I have been browsing the documentation but cannot find a Trilinos package that I believe will help me out. I looked at Belos, which appear to be close to what I need, but I'm not sure. Any suggestions?

Thanks,

Einar



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