Get Jacobian when using problem-based approach in Optimization Toolbox

When using lsqnonlin to solve a least squares problem, the jacobian gets returned as last argument:

[x,resnorm,residual,exitflag,output,lambda,jacobian] = lsqnonlin(___)

However, when using the problem-based approach, the jacobian isn't returned:

[sol,fval,exitflag,output,lambda] = solve(___)

Is there any way to get the jacobian also in this case?

Answer 1

[Alan Weiss]

Unfortunately, you cannot get the Jacobian output when using the problem-based approach. If you need it, then convert your problem using prob2struct and sove using lsqnonlin.

Alan Weiss

MATLAB mathematical toolbox documentation

[Philipp Glira]

Thank you.

I've tried to use the prob2struct. It works!

However, it seems that AD is used with solve(...), but not with lsqnonlin(...).

Here the output for solve(...)

Solving problem using lsqnonlin.

                                         Norm of      First-order 
 Iteration  Func-count     f(x)          step          optimality
     0          1         3.47967                           604
     1          2       0.0755244      0.0178525           2.96      
     2          3        0.075441    8.92775e-05       7.32e-05      
     3          4        0.075441    2.21069e-09       9.17e-12      

Optimization completed: The first-order optimality measure, 9.170276e-12,
is less than options.OptimalityTolerance = 1.000000e-06.

and here for lsqnonlin(...):

                                         Norm of      First-order 
 Iteration  Func-count     f(x)          step          optimality
     0          3         3.47967                           604
     1          6       0.0755244      0.0178525           2.96      
     2          9        0.075441    8.92774e-05       7.32e-05      
     3         12        0.075441     2.5088e-09       5.66e-08      

Optimization completed: The first-order optimality measure, 5.656498e-08,
is less than options.OptimalityTolerance = 1.000000e-06.

Is there any way to activate AD also in the lsqnonlin-Version?

I'm using the beta of Matlab 2021a.

[Alan Weiss]

You are quite right, AD does not apply to the lsqnonlin version. The only thing that I can think to try sounds terrible: run using solve first, then feed that solution as a starting point into lsqnonlin in order to get a Jacobian estimate.

By the way, if you are showing me results from your real problem, then the first-order optimality output shows that the Jacobian is either zero or you have some bound constraints.

Alan Weiss

MATLAB mathematical toolbox documentation