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Re: qp(): how do I get a simple inequality constraint?

From: Leo Butler
Subject: Re: qp(): how do I get a simple inequality constraint?
Date: Fri, 23 Sep 2011 09:46:27 -0400
User-agent: Gnus/5.110018 (No Gnus v0.18) Emacs/23.2 (gnu/linux)

forkandwait <address@hidden> writes:

> Hi all,
> I am trying to use qp to do an example in Caswell's Matrix Population Models
> 2001 (p147).  (I also know very little about optimization, so please bear with
> me.)
> Octave's qp seems to have different parameters than either ML's quadprog or
> Caswell's 2001 version of qp.  Since I don't really know what is going on, I 
> am
> trying to work the example "formally".
> Here is the set up.  The problem in Caswell is posed as:
> min (p'*G*p)/2 + f'*p
> subject to C*p <= b
> In his sample code to qp (with no initial guess of x0), that is written as:
> p = qp(G, f, C, b)
> However the Octave documentation states that with qp(X0,H,Q,A,B), A*x = b --
> i.e. that A and b define an EQUALITY constraint, not an inequality constraint.
> How do I get an inequality constraint like Caswell's, and make sure not to 
> have
> any equality constraints?  Do I use A_LB and set the other parameters == []?
> Thanks for any help!

You add a slack variable to your state, call it s. Your inequality

1)  C*p + s = b,

2)  s >= 0.

You can then use the LB/UB to enforce (2). I leave it to you to write
your original program with this extra slack variable.


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