fmincon computes all the outputs even with a failed step.

I have an objective function which I am trying to minimize. And I supply the gradient and Hessian along with my objective function. My function looks like

[f,g,h] = myfunc(x);

f = ...;

if nargout>1, g = ...; end

if nargout>2, h = ...; end

fprintf('%d\n',nargout); % I Want to see what outputs fmincon is asking for.

Initially, all the three (f,g,h) are computed as nargout = 3. After the step is calculated,i.e., during 2nd iteration, nargout is still 3 even though I see that the step is a failed step. That is f doesn't decrease using the correction but fmincon still asks to compute gradient and Hessian at this new value of x. Isn't this waste of time(as this value of x is rejected)? (Or) Is it possible to put a condition that gradient and Hessian should be computed only after the correction/step is valid?

Options I use are: Trust-region-reflective algorithm, with 'x' being constrained between some fixed bounds, on matlab2013b. And

options.GradObj = 'on'; options.Hessian = 'on';

Answer 1

[Pritesh Shah]

Hi,

First thing, there should be only one output value from your objective function for single objective function. https://in.mathworks.com/products/optimization/features.html#defining-and-solving-optimization-problems

[Walter Roberson]

No, if the appropriate options have been set, then the Jacobian or Hessian should be output by the objective function as well. See https://www.mathworks.com/help/optim/ug/writing-scalar-objective-functions.html#bu2w6a9-1

[Ravi Kumar Pallantla]

True, Jacobian or Hessian can also be outputs of objective function. I updated my question saying that I include them in my options.

[Walter Roberson]

Note: for trust-region-reflective, using option 'Hessian', 'on' requires that the third output of the objective function is the estimated hessian. trust-region-reflective always requires that the second output of the objective function is the gradient (that is, if you do not turn on the GradObj option then it will refuse to use trust-region-reflective)