How to replace my optimset with equivalent optimoptions ?

Hi all

using Fsolve, I am getting into difficulties and want to use Jacobian and Hessian as well , but first I need to pass from optimset to optimoptions

currently my Options are :

options = optimset('Display','iter','MaxFunEvals',1e6,'MaxIter',1e6,'TolFun',1e-3,'DerivativeCheck','on','Diagnostics','on');

so first, I need to have the equivalent optimoptions and then include Jacobian and Hessian.

since for some of my input data no solution is found ( Func-Count = 1.5e+7 ) , I need to imrpove my solution

Answer 1

[Matt J]

Why not just,

options = optimoptions(@fsolve, 'Display','iter','MaxFunEvals',1e6,'MaxIter',1e6,...
                       'TolFun',1e-3,'DerivativeCheck','on','Diagnostics','on');

[farzad]

thank you

what about Hessian and Jacob ?

[Matt J]

For the Jacobian, set 'SpecifyObjectiveGradient' to true, and follow instructions and examples here,

https://www.mathworks.com/help/optim/ug/fsolve.html#buta__s-fun

[farzad]

thank you

this is suggested in the page :

options = optimoptions('fsolve','SpecifyObjectiveGradient','on')

I get

Error: Invalid value for OPTIONS parameter SpecifyObjectiveGradient: must be logical TRUE or FALSE.

[Torsten]

options = optimoptions(@fsolve,'SpecifyObjectiveGradient',true)

[Matt J]

That is a documentation error. You should set to true.

[farzad]

that is as you said, the problem is that Matlab does not accept 'on' for Jacobian

[farzad]

Now I did :

 options = optimoptions(@fsolve,'Display','iter','MaxFunEvals',1e6,'MaxIter',1e6,'TolFun',1e-3,'DerivativeCheck','on','Diagnostics','on', 'SpecifyObjectiveGradient',true);

but now I get the error :

too many output arguments ! is the definition right ? and how to ask for more output arguments ?

[Matt J]

Without code and the full error message, the problem is undiagnosable. However, I suspect you forgot to provide the Jacobian computation in your objective function code.

[Torsten]

@farzad:

Did you ask for the number of output arguments in your code ?

https://de.mathworks.com/help/optim/ug/nonlinear-equations-with-jacobian.html

[farzad]

I can't share my full code. I hope this way I resolve it..

I have a bit of diffulty in using your link @Torsten , since I have defined my function in another m file and I call the

[x,fval,exitflag,output] = fsolve(fun,xstart,options);

in my main file. So based on this tutorial you shared, I should add thos Jacobian calc lines in the function definition m file ?

[Torsten]

Of course, where else ?

And with the if statement about the number of output arguments.

[farzad]

I didn't understand your last phrase

[Torsten]

Look at the function file provided in the link:

if nargout > 1 
   Supply Jacobian
end

[farzad]

And, why can't I just do : jacobian(f,x)

[Matt J]

jacobian(f,x) is a Symbolic Math Toolbox function. It only takes symbolic variables f and x as input and only returns symbolic results. And it is slow.

[farzad]

Thank you, but from the link you shared, I could not learn how to calculate my own function's Jacobian. Where did that 4 coefficient come from in the jacobian when all the main function coeffs are 3.

[Matt J]

From the terms.

[farzad]

Still not clear

I don't understand the C ,D and E matrix size selection , also in c ,d, and e

[farzad]

How about the following ?

[diff(f1,x), diff(f1, y); diff(f2, x), diff(f2, y)]

[Matt J]

No, diff(f1,x) is also a symbolic function. It is probably better for you to use the fundamental definition of the Jacobian,

https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant

to compute the Jacobian for your specific function.

[farzad]

Are you Sure diff is symbolic ?

and why can't I use symbolic ? shall you help me understand ?

[Matt J]

Do you understand the difference between symbolic and numeric computation? In symbolic computation, you present the expression for a function, and the software tries to take its derivatives analytically, as you or I would in a calculus course. The result is an analytical expression for the derivative, not a number.

But fsolve is a numeric solver. It puts in numbers for x and expects your code to give back numbers for the resulting Jacobian(x). On top of that, it does this repeatedly with different x, in its search for a solution. For the sake of speed, therefore, you don't want your code redoing the calculus to get expressions for the Jacobian every time it is called.