[Ipopt] Question About Augmented Matrix (KKT Matrix) in IPOPT

[Anil Rao]

All,

I have some questions regarding the KKT system that is being factorized by whichever linear solver is interfaced with IPOPT (Mumps, MA27, MA57).  The particular linear solver is not in question, it is the KKT matrix that IPOPT is sending to the linear solver.  Specifically, it says in Zavala's book, "Computational Strategies for the Optimal Operation of Large-Scale Chemical Processes" that IPOPT factorizes the augmented matrix, where the augmented matrix includes the barrier Hessian.  I want to know where the following quantities are computed in IPOPT:

(1) The actual Hessian, H_i
(2) The barrier Hessian, W_i, where W_i = H_i + Sigma_i
(3) Sigma_i, where Sigma_i = inverse(X_i)*V_i where X_i is a diagonal matrix of the current estimate of the decision vector and V_i is a diagonal matrix of the Lagrange multipliers of the simple bound constraints x_min <= x <= x_max

The reason I ask this question is that in some problems we are solving IPOPT appears to be sending to MA57 augmented matrices whose elements have extremely wide disparities in magnitude.  For example, in some problems which IPOPT seems to solve perfectly fine we are seeing many orders of magnitude difference in elements of the augmented matrix and we cannot understand why the elements are so widely separated in magnitude.  

In addition to the above requests, I am grateful if somebody can point me to the exact location in IPOPT where the augmented matrix is constructed and sent to the linear solver.  

Thank you for any help you can provide.

Regards,

Anil Rao



-- 
Anil V. Rao
Associate Professor
Department of Mechanical and Aerospace Engineering
University of Florida
Gainesville, FL 32611-6250
Tel:  (352) 672-1529
E-mail:  anilvrao at gmail.com
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