Store result from for-loop and plot

Hi,

I have a maximization problem which I want to solve in matlab. The problem consists of several parameters, but I am mostly interested in what happens to x when alpha increases from 0 to 0.5 with increments of 0.05. I then want to plot the value of x in a figure with x on the y-axis and alpha on the x-axis

I have defined the function in one file:

function b = maximizationpb2(x, alpha)
beta1 = 6;
beta2 = 6;
s1 = 1/3;
s2 = 1/3;
s3 = 1/3;
alpha = 0.5;
b = -(x(1) - beta1*((x(2)-s2)^2+(1-x(1)-x(2)-s3)^2))^(1-alpha) * (x(2) - beta2*((x(1)-s1)^2+(1-x(1)-x(2)-s3)^2))^alpha;

And then I have used fmincon to solve the problem:

lb = [0,0];
ub = [1,1];
A = [1,1];
b = [1];
Aeq = [];
beq = [];
x0 = [1/3, 1/3];
a = fmincon(@maximizationpb2,x0,A,b,Aeq,beq,lb,ub);
x3 = 1 - a(1) - a(2);

My first difficulty is to make a for loop which goes through all values of alpha = 0:0.05:0.5. I have to admit I have no clue where to start (I was so happy last week when I finally managed to solve the problem!!). Any help would be very much appreicated!

[Stephen23]

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
%--------------------------------------------------------------------------

Answer 1

[Torsten]

function driver
lb = [0,0];
ub = [1,1];
A = [1,1];
b = [1];
Aeq = [];
beq = [];
x0 = [1/3, 1/3];
for k=1:11
alpha(k)=0.05*(k-1);
a = fmincon(@(x)maximizationpb2(x,alpha(k)),x0,A,b,Aeq,beq,lb,ub);
M(k,1)=a(1);
M(k,2)=a(2);
M(k,3)= 1 - a(1) - a(2);
end
plot(alpha,M(:,1))  % plot a(1) over alpha

function b = maximizationpb2(x, alpha)
beta1 = 6;
beta2 = 6;
s1 = 1/3;
s2 = 1/3;
s3 = 1/3;
b = -(x(1) - beta1*((x(2)-s2)^2+(1-x(1)-x(2)-s3)^2))^(1-alpha) * (x(2) - beta2*((x(1)-s1)^2+(1-x(1)-x(2)-s3)^2))^alpha;

Best wishes

Torsten.

[charlotte88]

Thank you so much!!