# Why do I get no solution found in Fsolve despite the results match my nonlinear equations ?

13 views (last 30 days)
Edited: farzad on 8 Jul 2019
Hi All
I am solving a set of Non Linear equations. when I put the solution results in each of my equations, the result is zero or very close to zero ( 1e-15 as residual)
the options I use :
options = optimoptions(@fsolve,'Display','iter','MaxFunEvals',1e6,'MaxIter',1e6,'TolFun',1e-1,'DerivativeCheck','on','Diagnostics','on');
but on the message board I get the no solution found, that does not change with any tolerance value :
Here I put a copy of the last iterations and the message :
23 72 1.44467e+07 0.000238419 1.4 0.000238
24 73 1.44467e+07 0.000238419 1.4 0.000238
25 77 1.44467e+07 5.96046e-05 0.325 5.96e-05
26 78 1.44467e+07 5.96046e-05 0.325 5.96e-05
27 82 1.44467e+07 1.49012e-05 0.147 1.49e-05
28 86 1.44467e+07 1.49012e-05 0.0306 1.49e-05
No solution found.
fsolve stopped because the problem appears regular as measured by the gradient,
but the vector of function values is not near zero as measured by the
selected value of the function tolerance.
fsolve stopped because the sum of squared function values, r, has gradient with
relative norm 3.057666e-02; this is less than options.OptimalityTolerance = 1.000000e-01.
However, r = 1.444675e+07, exceeds sqrt(options.FunctionTolerance) = 3.162278e-01.
Optimization Metric Options
norm(grad r) = 3.06e-02 OptimalityTolerance = 1e-01 (selected)
r = 1.44e+07 sqrt(FunctionTolerance) = 3.2e-01 (selected)

@Bruno :
if you have 3 or 5 or 6 second order equations ,once you have the x matrix as the results of the solution , and if Matlab gives that large r = 1.444675e+07 in command prompt , what would you expect to get by running ( F9) each of your equations ?
@Bruno
is it an impossible question

Matt J on 7 Jul 2019
Edited: Matt J on 7 Jul 2019
You're asking for guesses? Because you are not plugging the solution into the same equations that were given to fsolve. fsolve thinks you have a residual norm of sqrt(1.44e+07).

Bruno, shall we avoid this way of conversation ?
you asked me to test fun(x) and tell you the output and I did
and reported you.
@Matt J
why do you avoid checking my last report where I have a small fun(x)
and a big error
they are not telling the same thing
Sorry
I was doing something wrong