[Ipopt] Matrix factorization as an optimization problem (?)
Tran Minh Tuan
tmtuan at laas.fr
Tue Mar 24 12:47:28 EDT 2009
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
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