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

[Frank J. Iannarilli]

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