MATLAB: Fminsearch with an integral function

fminsearchnumerical integrationoptimization

Hello!

I want to minimize a function with an integral using fminsearch. The question is that I dont know how to define it properly.

The function i want to minimize is:

I want to minimize it respective to θ being A,

given by the user before any calculation.

How can i define the function and the fminsearch procedure?

Thanks!

Best Answer

See this code

A = 1;
sigma0 = 2;
int_term = @(theta) integral(@(phi) 1/(sigma0*sqrt(2*pi))*exp(-1/2*(phi/sigma0).^2).*sin(theta-phi), 0, 2*pi);
obj_fun = @(theta) -A*cos(theta)+int_term(theta);
theta_sol = fsolve(obj_fun, 0)

Related Solutions

MATLAB: Solving non linear equation using fsolve

You are not passing theta_n and other parameters to root2d(). One fix is to make root2d a Nested Function. Also, you must choose a different initial point. phi0 = [10,10] worked for me.

function solve_it()
    beta_a = 10;
    alpha_n = 10 ;
    eta= 18;
    i = 18;
    theta_i = 10;
    theta_n = 10 ;
    
    fun = @root2d;
    phi0 = [10,10];
    phi = fsolve(fun,phi0);
    phi_n = phi(1),
    phi_i = phi(2),
    function F = root2d(phi)
    F = zeros(2,1);
    F(1) = (pi*sin((pi*(phi(1) + theta_n))/180)*cos((pi*phi(2))/180)*(cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180)))/(180*sin((pi*phi(1))/180)*(cos((pi*(phi(1) + theta_n))/180)*cos((phi(2)*pi)/180) + sin((phi(2)*pi)/180)*tan((theta_i*pi)/180))^2) - (pi*cos((pi*phi(1))/180)*(cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180)))/(180*sin((phi(1)*pi)/180)^2*(cos((pi*(phi(1) + theta_n))/180)*cos((pi*phi(2))/180) + sin((pi*phi(2))/180)*tan((pi*theta_i)/180)));
    F(2) = ((cos((pi*theta_n)/180) + tan((pi*i)/180)*tan((pi*theta_i)/180))*((pi*cos((pi*(phi(1) + theta_n))/180)*sin((pi*phi(2))/180))/180 - (pi*cos((pi*phi(2))/180)*tan((pi*theta_i)/180))/180))/(sin((pi*phi(1))/180)*(cos((pi*(phi(1) + theta_n))/180)*cos((phi(2)*pi)/180) + sin((phi(2)*pi)/180)*tan((theta_i*pi)/180))^2);
    end
end

MATLAB: Solving a matrix equation with a parameter in the coefficient matrix

syms theta S F
r = 0.025;
h = 0.3;
rho = 7850;
g = 9.81;
m = r^2 * pi * h * rho;
phi = atan((0.15 - 0.15*sin(theta))/(0.15*cos(theta)));
F_g = [0 , -m * g];
F_s = [-S*cos(phi), S*sin(phi)];
F_p = [F*cos(theta), F*sin(theta)];
eq(1) = F_g(1) + F_s(1) + F_p(1) == 0;
eq(2) = F_g(2) + F_s(2) + F_p(2) == 0;
eq(3) =  0.15*cos(theta)*F*sin(phi) - 0.15*sin(theta)*F*cos(phi) + m * g * 0.15 * cos(theta) == 0;
% New equations 
eqn(1) = lhs(eq(1)) == lhs(eq(3));
eqn(2) = lhs(eq(2)) == lhs(eq(3));
sol = solve(eqn,F,S)
pretty(sol.F)
pretty(sol.S)

Best Answer

Related Solutions

MATLAB: Solving non linear equation using fsolve

MATLAB: Solving a matrix equation with a parameter in the coefficient matrix

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