Q2. Why does SNOPT perform minor iterations on an unconstrained problem?

The QP sub problem sometimes does more than one minor iteration for each each major iteration. I had assumed that minor iterations are only possible when there are inequality constraints.

A2. SNOPT starts the first QP with all variables fixed at their initial values. These are known as "temporary bounds", or "temporary constraints". The first QP will perform minor iterations as these variables are allowed to change from their initial values.

Q3. Why does SNOPT sometimes do one or two minor iterations when my problem only has equality constraints?

A3. If the equations for the search direction are ill-conditioned, an iterative refinement scheme is used to improve the accuracy. The iterative refinement iterations are counted as minor iterations.

Q4. If I attempt to solve my problem using SNOPT, I get the error message: EXIT -- the current point cannot be improved. Is there a bug in SNOPT?

A4. This type of error is almost always caused by a problem with the model or calling subroutine. There are two steps that should be followed if this error occurs:

(a) Check your main program using some Fortran syntax checker. I strongly recommend FTNCHEK which is in the public domain and can be downloaded from various sites. See e.g., http://wwwcn.cern.ch/dci/asis/products/MISC/ftnchek.html, I never run a new code without using FTNCHEK first. It has saved me many months of painful debugging.

(b) If step (a) shows that your code is clean, try running SNOPT with the option "Verify level 3''. This will check that you have coded the derivatives correctly.

Q5. I have installed SNOPT on a DEC Alpha as directed in the README.install file. However, when running the tests, some of the problems fail to converge or get the wrong answer when I run through the standard cases. Can you offer any advice?

A5. The problem is most likely with the options that determine the level of compiler optimization. If the level is too high, you may see inconsistent results. For example, the following options do and do not work for SNOPT on a DEC Alpha:

Worked: -fast -O4 -tune host -inline all Failed: -fast -O5 -tune host -inline all

Q6. I am using a parameter estimation problem with SNOPT. In this type of problem the objective and constraints are both functions of a complicated vector-valued function v(x). SNOPT requires the objective and constraint functions to be defined in two separate subroutines. Although it is possible to compute the problem functions separately or pass information using the user workspace parameters cu, iu and ru, , this is either very complicated or expensive in CPU time. Is it possible to compute the objective and constraints at the same time?

A6. The distribution for SNOPT includes a subroutine SNOPTM that is equivalent to SNOPT except that the objective and constraint functions can be computed in the same subroutine.

Q7. I have just implemented a test version of my code, and I get the error message: 21 EXIT -- error in basis package. What am I doing wrong?

A7. This error is usually caused by an error in the definition of the input arrays a(*), ha(*), and ka(*).

Q8. The derivatives for my problem are very expensive and so I use the option ``Non derivative line search'' to reduce the number of times the derivatives are calculated. However, I notice that the number of derivative calculations doesn't seem to be any smaller. Why is this so?

A8. Two things need to be done when using a non derivative line search. First, the option ``Non derivative line search'' be set. Second, the user must skip the computation of the derivatives in funcon and funobj when SNOPT sets the input variable mode = 0.

Q9. I am using SNOPT to optimize a model that requires a significant amount of work to compute the objective gradient. In testing various scenarios, I would like to be able to fix some of the variables for a particular run.

My question is the following: do I have to provide the derivatives of the objective function with respect to the fixed variables, or can I simply use a dummy value for this gradient? Computing the fixed gradients exactly will mean considerable extra computation.

Of course, I can always discard the fixed variables from the problem given to SNOPT, but this will mean I will need to change the problem functions for each run.

A9. You can fix the jth variable at the value const by including the constraint bl(j) = bu(j) = const. If you assign a dummy value to gObj(j), it should not make any difference to the run, except that the reduced costs (i.e., Lagrange multipliers) for any fixed variables will be meaningless.

If you leave the gradient undefined (i.e., you don't set the components of gObj associated with the fixed variables) then SNOPT will compute them by finite differences: gObj(j) = (fObjJ - fObj)/delta, where fObjJ is fObj evaluated at the perturbed point x + e_j delta. I assume that you DON'T want to do this!