[Ipopt] Matrix factorization as an optimization problem (?)

[Tran Minh Tuan]

Hi all,

Following the previous question, I formulated the problem differently  
in order to have another optimization problem.
In this case there are 2000 constraints and the result is:

===
Number of nonzeros in equality constraint Jacobian...:    40000
Number of nonzeros in inequality constraint Jacobian.:        0
Number of nonzeros in Lagrangian Hessian.............:        0

Exception of type: TOO_FEW_DOF in file "../../../../Ipopt/src/ 
Interfaces/IpIpoptApplication.cpp" at line 668:
  Exception message: status != TOO_FEW_DEGREES_OF_FREEDOM evaluated  
false: Too few degrees of freedom (rethrown)!

EXIT: Problem has too few degrees of freedom.
===

In the documentation of Ipopt, it is said that it is likely that  
there were too many constraints but I don't know "how many is too  
many ?".

In fact, the problem that I try to solve is a matrix factorization  
problem: given m,n,r as matrix sizes and matrix V (m x n), find W (m  
x r) and H (r x n) such that V = W*H.
This is not really a non-negative matrix factorization problem  
because V is not supposed non-negative (however, H must be non- 
negative as constraints, W is free).

Thank you for your discussion,
Minh