nonlinear constraints in fmincon

Hi all,

I have a function "myfunc" to minimize subject to a set of nonlinear constraints written in a function "myconstr". The problem is that myfunc is expensive to evaluate and "myconstr" uses as one of its inputs, the output of "myfunc". How can I deal with this problem efficiently if I want to use fmincon as the optimizer?

Here are some avenues that I am looking into but I am not satisfied with them:

1. It is possible to write myconstr so that it re-evaluates myfunc but this would slowdown things even more.
2. do the opposite: evaluate myconstr within myfunc and use a global variable, which I am reluctant in doing.

any ideas?

Thanks,

Pat.

Answer 1

[Alan Weiss]

There is a section in the documentation dealing with exactly this issue.

Alan Weiss

MATLAB mathematical toolbox documentation

[Patrick Mboma]

This is excellent. Thank you very much Alan.

Answer 2

[Ryan Livingston]

You could make a little wrapper around myfunc which maintains a previous value...or values

function out = callMyfunc(arg1, arg2)
  persistent oldVal;
  if isempty(oldVal)
    oldVal = cell(1,2);
    oldVal{1} = {arg1, arg2};
    oldVal{2} = myfunc(arg1, arg2);
    out = oldVal{2};
    return;
  end
  % Check to see if we've evaluated this one before
  if (isequal({arg1, arg2}, oldVal{1}))
    out = oldVal{2}; %Use stored value
  else
    out = myfunc(arg1, arg2);
  end

Alternatively, I could imagine just making a handle class which maintains the old values and passing that in and out of the calls to callMyfunc if you don't like the persistent idea. Then, you attempt to record each evaluation if the lookup fails.

[Patrick Mboma]

Hi Ryan,

Thank you for the answer. In my opinion, persistent, global and handle all do the same thing, some of them are just much "cleaner" than the others but there is a price to pay in all of them. For the persistent example, I anticipate that a lot of time will be spent in evaluating "isequal({arg1,arg2},oldVal)"

In my ideal world, myfunc would return both its function value and the function value of the constraints. Until I find a better workaround, I am going to implement your persistent idea and see what it gives.

Thanks,

Pat.