# Way to solve these non-linear equations since fsolve isn't working fine.

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function F = Glc_Gal_Lac(y,u,gal,lac)

Yx_Gal = 138000000;

KGal = 18.23;

Yx_Glc = 1010000000;

mGlc = 0.0000000000343;

fGal = 0.35;

KcGal = 5.27;

Yx_Lac = 54000000;

YLac_div_Glc = 1.56;

Lac_max1 = 21.20;

Lac_max2 = 16;

mLac = 0.000000000187;

F(1) = y(1) - (((-1*(u/Yx_Glc)) - mGlc)*((KcGal/(KcGal + gal)).^(1 - ((fGal*y(1))/y(2))))); % qGlc

F(2) = y(2) - (-1*(u/Yx_Gal)*(gal/(gal + KGal))); % qGal

F(3) = y(3) - (((u/Yx_Lac) - (YLac_div_Glc*y(2)))*((Lac_max1 - lac)/Lac_max1)) + ((mLac*(Lac_max2 - lac))/Lac_max2); % qLac

end

I believe the above function is understandable, now upon solving it what I get is

Equation solved at initial point.

fsolve completed because the vector of function values at the initial point

is near zero as measured by the value of the function tolerance, and

the problem appears regular as measured by the gradient.

<stopping criteria details>

Error using fsolve (line 300)

Objective function is returning undefined values at initial point. FSOLVE cannot continue.

AND

Equation solved. The final point is the initial point.

The sum of squared function values, r = 6.140730e-22, is less than sqrt(options.FunctionTolerance) = 1.000000e-03.

The relative norm of the gradient of r, 4.417532e-11, is less than options.OptimalityTolerance = 1.000000e-06.

Now how to make this work, I have tried changing initial points. Plotting the function is difficult since other variables inputted are linked here and there. So, any alternate way you can suggest or any editing in code will be a great help for me to make it run successfully.

##### 4 Comments

J. Alex Lee
on 7 Jun 2021

your anonymous function looks messed up:

@(y) Glc_Gal_Lac(x,u,gal,lac)

should probably be

@(y) Glc_Gal_Lac(y,u,gal,lac)

Anyway you have tiny numbers and enormous numbers, which could be problematic and leading to numerically too-small residuals

Walter Roberson
on 9 Jun 2021

### Answers (1)

Chidvi Modala
on 9 Jun 2021

The objective function supplied to FSOLVE must return a vector without any Inf or NaN entries. In your case, it is possible that objfun(xo) returns a NaN or errors out (where "objfun" is objective function and "xo" is the initial point). To avoid this error, you need to choose a better initial point.

You may refer to documentation for FSOLVE: http://www.mathworks.com/help/optim/ug/fsolve.html

This applies to other functions as well, such as LSQNONLIN.

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