Using Fminsearch to solve equation

Hello,

I need your help to use fminsearch to solve this equation, I did not know how to solve it, because I'm a beginner in Matlab.

Best regard,

Answer 1

[Walter Roberson]

Generally speaking,

f(x) = constant

can be solved by minimizing

(f(x) - constant)^2

This approach can be used with multiple variables.

The difficulty is in finding a starting point for the search. Different minimizers have different algorithms but in practice all of the local minimizer can get stuck in local minima. (Theory does say that Simulated Annealing will find the global minimum if given enough time but the time required might be many times the expected lifetime of the Universe)

[Walter Roberson]

Also, I have never quite trusted that theory that Simulated Annealing will eventually find the answer: it smells to me too much like the theory that a random walk will definitely return to the origin if let run infinitely long, which has been disproven for more than 2 dimensions. https://mathoverflow.net/questions/45098/when-do-3d-random-walks-return-to-their-origin

[MAROUANE ENNAGADI]

Thank you so much for your reponse, I tried to solve it and I find some errors:

% Main Principal :
% Données:
sigma=0.1;
e=1.6e-19;
N=10.^26;
E_LUMO=0;
K_B=8.625e-5;                     % Constante de Boltzman 
T=300;                            % Témperature Ambiante
Bc=2.735;
Alpha=0.215*N.^(-1./3);           % the localization length
Ef=E_LUMO-0.5;                    % Energie de Fermi
% Valeur de départ Et0 :
E_t_0=0;
% Bornes d'integration en Energie:
E1=-10*sigma; 
N_0=1000;
E=linspace(E1,Et,N_0);
% Calcul de Et:
Et=fminsearch('F_min',E_t_0,[],Bc,K_B,T,Alpha);

My Fonctions are :

function [Gauss]=densite_Gaussienne(N,sigma,E,E_LUMO)
Gauss=N./(sigma*sqrt(2*pi)).*exp(-(E-E_LUMO).^2./(2*sigma^2));
end
 function [S_F_D]=statistque_Fermi_Dirac_1(E,Ef,K_B,T)
 S_F_D=1-(1./(1+exp((E-Ef)./(K_B*T))));
 end
 
 function [Multi_G_F_D]=multiplication_G_D_1(Gauss,S_F_D)
 Multi_G_F_D=Gauss.*S_F_D;
 end
 
 % Calcul de nt:
function [nt]=n_t_1(E,Multi_G_F_D)   
nt=trapz(E,Multi_G_F_D);
end

function F=F_min(Et,Bc,K_B,T,Alpha,E1,N_0)
E=linspace(E1,Et,N_0);
nt=trapz(E,Multi_G_F_D);
F=abs((2/3)*(4.*pi/3*Bc).^-1/3.*(K_B*T./Alpha).*(nt).^-4/3.*(1-(1./(1+exp((Et-Ef)./(K_B*T)))).*(N./(sigma*sqrt(2*pi)).*exp(-(Et-E_LUMO).^2./(2*sigma^2))))-1);
end

Best regard,

[Walter Roberson]

http://www.mathworks.com/help/matlab/math/parameterizing-functions.html