I am getting this error while solving "fsolve stopped because it exceeded the function evaluation limit,

file 1

   % model 2 main part, cal & plot
  tic;

N = 10;          % N = 20 
lambda = 0.1:1;
S = [1:50];  

PL = 1024;

for i = 1:50
    x0 = [1; 1; 1; 0;   1; 0; 1346; 0.0027];   % wired start point 
    options = optimoptions('fsolve'); 
    [x,fval] = fsolve(@(x)m2_numeric_solver2(x,N,lambda(i)),x0,options);  

      Data = x(5) * x(6) * PL;
      Time = x(7);
      S(i) = (Data / Time)/10^6;

      formatSpec = 'iteration %d complete\n';
      fprintf(formatSpec,i)
  end

plot(S);
title('Unsaturation throughput vs arrival rate');
xlabel('arrival rate');
ylabel('saturation throughput');
grid on;

toc;

file 2

% model 2 numberic solver with capture effct and error rate

% x(1) --  tao
% x(2) --  Pcol
% x(3) --  Peq
% x(4) --  Pcap

% x(5) -- Pt
% x(6) -- Ps
% x(7) -- E[T]
% x(8) -- q

% notice: warning i, confuse with complex 'i'
% notice: double for symsum

function F = m2_numeric_solver2(x,N,lambda)
syms k;
z = 4;                %  << capture threshold
W = 32;
m = 5;
Pe = 0.01;             % << channel error rate

tao = 1/(10^6);
Ts = 1140/(10^6);
Tc = 1364/(10^6);
Te = 1364/(10^6);

F = [     
     x(1) - 2*(1-2*x(3))*x(8) / ( x(8)*( (W+1)*(1-2*x(3)) + W*x(3)*(1 - (2*x(3))^m))   ...
     +  2 * (1-x(8)) * (1-x(3)) * (1-2*x(3)) );  

       x(2) - ( 1 - (1-x(1)) ^ (N-1) - x(4) );
       x(3) - ( x(2) + Pe - Pe*x(2) );
       x(4) - double( symsum( nchoosek(N,k+1) * x(1)^(k+1)*(1-x(1))^(N-k-1) / (1+z)^k, 1, N-1) ); 

       x(5) - (1 - (1 - x(1))^N);
       x(6) - (N*x(1)*(1-x(1))^(N-1) + x(4)) / x(5);
       x(7) - (  (1-x(5))*tao + x(5)*(1-x(6))*Tc + x(5)*x(6)*Pe*Te + + x(5)*x(6)*(1-Pe)*Ts );
       x(8) - (1 - exp(-lambda*x(7)) );     
  ];
  end

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Walter Roberson]

options = optimoptions('fsolve'); 
options.MaxIterations = 1000;
options.MaxFunctionEvaluations = 5000;

[Pankaj Khatiwada]

Thanks for your help appreciated...

Answer 2

[Alan Weiss]

You wrote

lambda = 0.1:1;

This gives the same value as

lambda = 0.1;

Later you call lambda(i) for i from 1 through 50. This makes no sense. Maybe you meant

lambda = linspace(0.1,1,50);

I would try to not use symbolic variables inside the objective function. If you really need them, perhaps use matlabFunction to convert any symbolic function into a numeric function before you use it. See Using Symbolic Mathematics with Optimization Toolbox™ Solvers.

One more thing: don't set options inside the for loop. Set them at the beginning, before the loop, because setting options is slow.

Alan Weiss

MATLAB mathematical toolbox documentation