Rank Deficient Warning from fmincon

Hello,

I'm trying to run an optimization using fmincon and the 'sqp' algorithm. The problem uses linear equality constraints, nonlinear equality constraints, and nonlinear inequality constraints along with upper and lower bounds which can be a combination of scalars or Inf values.

Occasionally I will receive this warning in the command window (or something similar):

Warning: Rank deficient, rank = 41, tol =  6.141450e-15. 
> In C:\Program Files\MATLAB\R2013a\toolbox\optim\optim\private\stopTestSQP.p>stopTestSQP at 204
  In C:\Program Files\MATLAB\R2013a\toolbox\optim\optim\sqpLineSearch.p>sqpLineSearch at 363
  In fmincon at 910
  In ZcompTrajectory at 78

Despite the warnings, the results from fmincon seem to be okay however. But the warning is a concern for me. I also occasionally get singular matrix warnings.

I've attempted to backtrace the warning but cannot see inside stopTestSQP or sqpLineSearch because they are p-code. The inputs to sqpLineSearch seem okay and I cannot identify any major difference between inputs to this function that work fine and those that produce a rank deficient warning.

The objective and nonlinear constraint functions are not producing "NaN" or "Inf" values. If I use active-set algorithm it seems to reduce if not eliminate how often I get rank deficient warnings.

Any suggestions on where to look? Thank you.

Answer 1

[Alan Weiss]

You can try some of the suggestions in the documentation for verifying that the result is sensible.

Alan Weiss

MATLAB mathematical toolbox documentation