SNOPT and MINOS solver message

[k.ka...@googlemail.com]

Hello everyone,

Thanks for your earlier comment.

My previous problem gave me the following message:
MINOS: infeasible problem (or bad starting guess).
44 iterations
Nonlin evals: constrs = 12, Jac = 11.

So MINOS couldnt solve it.


The problem now solves with SNOPT with message
Nonlinear infeasibilities minimized.
Nonlin evals: constrs = 2, Jac = 1.

Can this solution accepted to be near optimal? Is it an acceptable
solution? What does the message really mean?

Regards

[Michael A. Saunders]

Dear k,

The SNOPT message you received normally means that
the nonlinear constraints in your model cannot be
satisfied. A set of nonlinear constraints is treated
as c(x) - s = 0 with bounds on s (say l <= s <= u).
If xk is the current approximate solution, SNOPT forms
the linearization of the constraints:

c(xk) + J(xk)*(x - xk) - s = 0, l <= s <= u,

where J(xk) is the Jacobian (the matrix of constraint
gradients) evaluated at xk. The linearized constraints
could be infeasible if xk is a "bad" point (the Jacobian
has extreme values there), or if the original problem
really is infeasible.

The constraints are linearized at each "major iteration".
At any stage, if the linearized constraints are infeasible,
SNOPT introduces "elastic variables" for each nonlinear
constraint. The original problem is regarded as

min f(x) + w*sum(v) + w*sum(w)
st c(x) + v - w = 0, l <= s <= u, v,w >= 0
(plus any linear constraints),

during further major iterations, where w is a positive weight
that gets increased in stages if v and w don't decrease to
zero. If w is eventually increased to 1e+10 and v and w
are still nonzero, SNOPT terminates with that message,
meaning that the sum of v and w has been made as small as
SNOPT can manage, and the original problem appears to be
infeasible.

The only doubt in your case is that not all of this could
happen with only 1 Jacobian evaluation(!). But certainly
you should not conclude that you have a final point that's
anywhere near an optimal solution.

You will learn more about what the solvers think if you
find out how to save their iteration log. (It's called
the Print file for MINOS and SNOPT.)

From memory there were questions for you last time
about plausible bounds on your variables. You'll get
more help if you try to answer such questions, and perhaps
even more help if you post your model and some enthusiastic
reader feels like running it through AMPL.

Regards,
Michael