Fsolve with different combinations of parameters

Hi,

I have a system of 11 nonlinear equations and 11 unknown variables that I would like to solve for. The nonlinear equations also depend on a set of parameters. Using the fsolve function, I keep getting the message:

Solver stopped prematurely.

fsolve stopped because it exceeded the function evaluation limit,

options.MaxFunctionEvaluations = 8.000000e+03.

I therefore want to nest the fsolve function inside a set of loops over different combinations of parameter values to see if I can get a solution with a different set of parameters. What is the generic code for doing so?

Thank you very much!

Answer 1

[Torsten]

Varying the initial values for the unknown variables should be the first step. Try "MultiStart".

Varying parameters is usually done via nested for-loops where each loop runs over the values of one of the parameters.

[Selim Elbadri]

Hi Torsten,

Thank you for your response. Say that I know that not all parameter values will yield a solution. How would I adapt the code to loop over different parameter values?

Say the code is as follows:

zg = [1;..;1];
options=optimset('TolFun' , 1e-6,'Display','iter', 'TolX' , 1e-8, 'MaxFunEvals' , 8000, 'MaxIter' , 80000);
z = fsolve(@FUN,zg,options);

Then in the function file:

% Solve for equilibrium
function fval=FUN(z)

%List parameter values
parameter1 = 1
parameter2 = 2
.
.
.

%List unknowns
x1 = z(1)
x2 = z(2)
.
.
.

%List equations
fval(1) = ...
fval(2) = ...
.
.
.

Thank you!

[Walter Roberson]

Note: the number of iterations will never be greater than the number of function evaluations, so if you want to use different limits for the two your maximum evaluations should be at least as large as the maximum iterations

[Walter Roberson]

Detect failure by requesting at least three outputs from fsolve, and checking whether the third output (exitflag) is < 0

[Torsten]

zg = [1;..;1];
options=optimset('TolFun' , 1e-6,'Display','iter', 'TolX' , 1e-8, 'MaxFunEvals' , 8000, 'MaxIter' , 80000);
parameter1 = [1 2 3];
parameter2 = [0.1 0.2 0.3];
...
for ip1 = 1:numel(paramater1)
  for ip2 = 1:numel(parameter2)
    ...
    parameter = [parameter1(ip1);parameter2(ip2);...];
    [z(ip1,ip2,...),fval(ip1,ip2,...),exitflag(ip1,ip2,...)] = fsolve(@(x)fun(x,parameter),zg)
    ...
    end
end
    
% Solve for equilibrium
function fval = FUN(z,parameter)
  %List parameter values
  parameter1 = parameter(1);
  parameter2 = parameter(2);
  ...
  %List unknowns
  x1 = z(1)
  x2 = z(2)
  ...
  %List equations
  fval(1) = ...
  fval(2) = ...
  ...
end

[Selim Elbadri]

Hi,

When I run the code, I get the following error code:

Unable to perform assignment because the left and right sides have a different number of elements.

Unable to perform assignment because the indices on the left side are not compatible with the size of the right side.

Error in solution_loops (line 14)

z(ip1,ip2) = fsolve(@(x)FUNS(x,parameter),zg);

Caused by:

Failure in initial objective function evaluation. FSOLVE cannot continue.

My code is as follows:

% Solve for equilibrium
clear all

c_bar = [0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40];
beta = [0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4];

zg = [0.1;0.1;0.3;0.3;0.2;0.2;1.0;0.5;2.0;10.0;5.0];
options=optimset('TolFun' , 1e-6,'Display','iter', 'TolX' , 1e-8, 'MaxFunEvals' , 30, 'MaxIter' , 20);

for ip1 = 1:numel(c_bar)
  for ip2 = 1:numel(beta)
    
     parameter = [c_bar(ip1);beta(ip2)];
     z(ip1,ip2) = fsolve(@(x)FUNS(x,parameter),zg);

 end
end


function fval=FUNS(z, parameter)

c_bar= parameter(1);
beta = parameter(2);


cm = z(1);
.
.
.

fval(1)  = cm - (((ps*c_bar) + ((beta*Nm)/(1-beta)) + beta*Lps*Ns*ps^(1/beta) + beta*Lpm*Nm)/(1 + ps^(1-sigma)));
.
.
.

[Torsten]

Since z is a solution vector with more than one element, you will have to use

z(:,ip1,ip2) = fsolve(@(x)FUNS(x,parameter),zg);

instead of

z(ip1,ip2) = fsolve(@(x)FUNS(x,parameter),zg);

If you still get the error message

Failure in initial objective function evaluation. FSOLVE cannot continue.

try to evaluate your function with the initial values zg before calling "fsolve":

FUNS(zg,parameter)

Answer 2

[Walter Roberson]

Increase the maximum evaluations instead.

opts = optimoptions(@fsolve, 'MaxFunctionEvaluations', 1e5, 'MaxIterations', 1e5);

[bestx, fval, exitflag] = fsolve(HANDLE, x0, opts)