Function lsqnonlin() has no optimization effect

It is a teaching example, but I can't get the right answer in my software. How can I solve this problem?

[Ang Feng]

Well, I tried the code, and it produce

x =

    0.2578    0.2578
resnorm =

  124.3622

also with the warning information as well

Local minimum possible.

lsqnonlin stopped because the size of the current step is less than

the value of the step size tolerance.

<stopping criteria details>

Perhaps, we can ignore this warning.

[Matt J]

@Yuwen,

Please do not post your code as an embedded image. We cannot conveniently copy-paste it in that form.

@Ang Feng,

It is not a warning. It is an announcement of success! (Or at least, lsqnonlin believes that it was successful).

[Yuwen Zhu]

@Matt J@Ang Feng Thanks for your answers. I try this code again, and it works right.

[Yuwen Zhu]

And I have another question. My code has no optimization effection.

function f=objfunc(x)
PNO=[60.8,60.8,60.8,60.8,60.8,60.8,15.2,30.4,60.8,121.59,151.99,202.65,60.8,60.8,60.8,60.8,60.8];
PO2=[253.3,506.6,1013.3,2026.5,5066.3,10132.5,2026.5,2026.5,2026.5,2026.5,2026.5,2026.5,2026.5,2026.5,2026.5,2026.5,2026.5];
rNO=[7.12e-05,9.66e-05,1.31e-04,1.77e-04,2.66e-04,3.60e-04,5.32e-05,9.72e-06,1.77e-04,3.25e-04,3.948e-04,5.07e-04,1.79e-04,1.77e-04,1.79e-04,1.76e-04,1.79e-04];
a=log(PNO);
b=log(PO2);
y=log(rNO);
f=x(1)+a*x(2)+b*x(3)-y;

x0=[-16.800207,1.2008,0.4151];
[x,resnorm]=lsqnonlin(@objfunc,x0)

Local minimum found.

Optimization completed because the size of the gradient is less than
the value of the optimality tolerance.

<stopping criteria details>

x =

  -16.8802    1.2008    0.4151


resnorm =

    4.4249

Answer 1

[Matt J]

And I have another question. My code has no optimization effect

In this case, your initial guess already is optimal. You can see this by solving for the optimum x analytically, which is possible in this case because your model is linear, and because you have no bound constraints:

a=log(PNO(:));
b=log(PO2(:));
y=log(rNO(:));

x=[ones(size(a)),a,b]\y(:)

x =

  -16.8802
    1.2008
    0.4151