WG: [Coin-ipopt] Re: Help explaining IP/barrier, visualizing solver?

[Claas Michalik]

Hi,

Steinar Hauan is currently working on some Makefiles for the interface,
so that we hopefully will be able to release a first beta version shortly.
Anyway, since all of us have a lot of other stuff to do and even minor
bugs may take some time to be sorted out, we cannot yet
give a concrete date for the beta release, so please be patient ;-)

Regards, 

Claas

----- Originalnachricht -----
Von: "Frank J. Iannarilli" <franki at aerodyne.com>
Datum: Montag, Juni 13, 2005 2:44 pm
Betreff: [Coin-ipopt] Re: Help explaining IP/barrier, visualizing solver?

> Hi,
> 
> 
> Well, regarding my posting, I've since sleuthed about for some 
> answers. 
> Please tell me, dear reader, if what I've found below in fact rings 
> true.
> 
> One helpful pointer is the explicit link between barrier and 
> interior point 
> methods. I had been uncomprehendingly equating them. They are 
> equivalent, 
> but spring from differing root motivations:
> 
> <http://iridia.ulb.ac.be/~fvandenb/mythesis/node44.html>
> 
> 
> In essence, the barrier parameter u, applied to the barrier terms 
> for the 
> (primal) variable bounds inequalities in a barrier formulation, and 
> the 
> "complementarity perturbation parameter" t, replacing the equality 
> to zero 
> in the KKT relations for the Lagrangian formulation, are 
> structurally the 
> same thing.
> 
> 
> Yet the two approaches, namely the barrier formulation and the 
> primal-dual 
> formulation also differ.  The former requires a feasible starting 
> point, 
> and iterates that must remain feasible.  The latter allows 
> infeasible start 
> and iterates.
> 
> 
> Also, I had not realized that the term "interior point" method 
> pertains to 
> the maintenance of primal or primal-dual iterates within the 
> *variable 
> bounds*, and DOES NOT (for equality constraints) pertain to the 
> feasible 
> region.
> 
> ++++++  Remaining Questions (for me)  +++++++
> 
> ===>> Can anybody indicate the motivation for introducing the 
> "complementarity perturbation parameter" t?  Why not relax the 
> remaining 
> KKT conditions as well?
> 
> 
> 
> Regards,
> 
> 
> 
> Frank J. Iannarilli, franki at aerodyne.com
> Aerodyne Research, Inc., 45 Manning Rd., Billerica, MA 01821 USA
> www.aerodyne.com/cosr/cosr.html
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>