nonlinear minimization with fminunc

Hi All:

I am doing parameterization by minimizing a nonlinear target function. However, after the iteration runs, it returns the following message. And returns with the initial values for the parameters that I set.

 *Iteration  Func-count       f(x)        Step-size       optimality
     0           9          1.46536                      7.77e+06
     1         144          1.39431    1.57417e-14       5.47e+06

Local minimum possible.

fminunc stopped because the size of the current step is less than the default value of the step size tolerance.*

There is no error in the code. What do you suggest to solve this issue?

Thank you!

Answer 1

[Matt J]

Evaluate the gradient at the initial point and see if it is close to zero. Also, call fminunc with all of its output arguments,

[x,fval,exitflag,output,grad,hessian]= fminunc(...)

to get more diagnostic information.

[Daniel]

Thanks for your comments.

Gradient: 1.1230 -0.5735 -0.7339 -2.8473 -0.4665 -0.7594 -1.5631 -2.0650

Hessian: -0.3929 -0.0146 1.6484 1.8609 1.4881 2.0857 -0.6735 2.4585 -0.0146 1.9118 4.0316 3.6329 2.6916 2.6806 -0.9732 6.1937 1.6484 4.0316 0.3282 0.9016 1.4807 4.5981 -1.3104 3.2933 1.8609 3.6329 0.9016 3.0804 3.2111 2.4965 1.9743 0.3590 1.4881 2.6916 1.4807 3.2111 0.5078 1.3144 0.0943 1.4038 2.0857 2.6806 4.5981 2.4965 1.3144 2.8224 0.0054 1.7383 -0.6735 -0.9732 -1.3104 1.9743 0.0943 0.0054 1.2775 3.2253 2.4585 6.1937 3.2933 0.3590 1.4038 1.7383 3.2253 2.3437

How do you think?

Thanks!

[Matt J]

I'm guessing your function may not be differentiable. A local minimum of a twice continuously differentiable function should have a positive semi-definite Hessian and gradient near zero. It appears you are far from either.

Answer 2

[Shashank Prasanna]

The optimization stopped because size of the current step is less than the default value. However you can change the defaults.

I suggest you read the following articles in the link below:

http://www.mathworks.com/help/optim/improving-results.html

• When the Solver Fails
• When the Solver Might Have Succeeded
• When the Solver Succeeds

There are guidelines on what you can try in each of the situations.

[Daniel]

Thanks Shashank. I actually noticed that and fixed it with changing the default step size. But now, got another message:

fminunc stopped because it cannot decrease the objective function along the current search direction.

... looked online support, feels like there is really no solution for this...

Do you have any idea about this?

Thanks!

[Shashank Prasanna]

fminunc is a derivative based optimizer. If you have discontinuous objective surface or have multiple optimums then fminunc becomes sensitive to initial start points. If you do have an exotic objective function I recommend trying multistart or patternsearch which does better at finding "global" optimum solutions.

Local vs Global:

http://www.mathworks.com/help/gads/what-is-global-optimization.html#bsbaljn