You have alpha as a function input, but never use it. YOu need to change your function and learn to test your code:
function out = test
lb = [0,0];
ub = [1,1];
A = [1,1];
b = [1];
Aeq = [];
beq = [];
x0 = [1,1]/3;
s = [1,1,1]/3;
beta = [6,6];
alpha = 0:0.05:0.5;
out = NaN(numel(alpha),1);
for k = 1:numel(alpha)
a = fmincon(@(x)fun(x,alpha(k),beta,s),x0,A,b,Aeq,beq,lb,ub);
out(k) = 1 - a(1) - a(2);
end
end
%--------------------------------------------------------------------------
function b = fun(x, alpha, beta, s)
b = -(x(1) - beta(1)*((x(2)-s(2))^2+(1-x(1)-x(2)-s(3))^2))^(1-alpha) * (x(2) - beta(2)*((x(1)-s(1))^2+(1-x(1)-x(2)-s(3))^2))^alpha;
end
%--------------------------------------------------------------------------
