Where I make a mistake with fminimax?

Dear colleagues,

I have problem with optimisation function fminimax, which I use as a variant for regression analyses made by Curve fitter.

In the attached file are the vectors for x, y and z = f(x,y).

My code is, as follow. Sorry, I don't know how to paste it in appropriate format:

"

x=x_vremetraene;
y=y_period_pretovarvane;
z=z_111;
f = @(p) abs(p(1)*(p(2)+y).^p(3)./(x+p(4)).^p(5) - z);
F = @(p) reshape(f(p),[],1);

p0 = [1 1 1 1 1];

F(p0)

ans =

1.0e+02 *

2.314576069270182

2.796122919180851

3.081916551260510

3.284514792242277

3.441464927295814

3.926826269823946

1.650257401771352

.............................

by this point everything is good

format long
[p,fval] = fminimax(F,p0)

Local minimum possible. Constraints satisfied.

fminimax stopped because the size of the current search direction is less than

twice the value of the step size tolerance and constraints are

satisfied to within the value of the constraint tolerance.

<stopping criteria details>

p =

1.0e+03 *

-0.320589519017169 -2.281076321933144 -0.703130918618337 -0.366998883941303 1.591728772382496

fval =

1.0e+02 *

2.317909402603515

2.801122919180851

3.088583217927177

.........

"

The expected values for fval should be about 20. But they are as large as input z data.

Local minimum possible. Constraints satisfied.

I have tried p = lsqnonlin(F,p0) for preestimation of the parameters p

but it also gives me an error message.

Error using lsqncommon (line 38)

Objective function is returning Inf or NaN values at initial point. lsqnonlin cannot continue.

Error in lsqnonlin (line 264)

lsqncommon(funfcn,xCurrent,lb,ub,options,defaultopt,caller,...

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

[Walter Roberson]

When you use unconstrained search then p(4) can happen to become the negative of some x value, leading to a division by 0

[Torsten]

The matrix z_111 you use for fitting contains NaN values.

[Boyan]

Hi, Walter and Torsten,

Torsten is right. The problem is that fminimax does not work with NaN values, unlike Curve Fitter app, where NaN is not a problem.

Answer 1

[Matt J]

Some ideas,

1. The choice of initial guess p0=[1,1,1,1,1] looks arbitrary. I don't see why that would be a good guess.
2. You shouldn't be using abs() in the objective function. Possibly, you intended to use the AbsoluteMaxObjectiveCount option.
3. Once you've removed abs(), you will need something to keep the fresult of F(p) real-valued, which means you probably need to apply constraints and bounds on p. The exponentsp(3) and p(5), for example, probably need to be constrained non-negative.

[Boyan]

Hi, Matt,

Thank you for your answer. Maybe be your instructions could be usefull at second stage, as far as the problem was, as Torsten said, the NaN values in z matrix.