Converged to an infeasible point. fmincon stopped because the size of the current step is less than the default value of the step size tolerance but constraints are not satisfied to within the default value of the constraint tolerance.

N = 2; % Number of mass points
X0 = rand(1,N);
p0 = ones(1,N)/N;
x0 = [X0 p0];
n = 1;
lb = zeros(length(x0),1);
ub = ones(length(x0),1);
Aeq = [zeros(1,length(x0)); ones(1,length(x0))];
beq = [1 1];   
% nonlcon = @unitdisk
[x_star,~,exitflg] = fmincon(@(x) myfunct12(x,n),x0,[],[],Aeq,beq,lb,ub);
while exitflg ~= 1
    X0 = rand(1,N);
    p0 = ones(1,N) / N;
    x0 = [X0,p0];
    [x_star,~,exitflg] = fmincon(@(x) myfunct12(x,n),x0,[],[],Aeq,beq,lb,ub);
end

% x = fmincon(@(x) myfunct12(x,n),x0,[],[],Aeq,beq,lb,ub)
% x
x_star;
myfunction is
function [z] = myfunct12(x,n)
 

y = 0:1:n;



p_y_x = zeros(n,n+1);
h_y_x = [];



for i=1:n
    for k =1:length(y)
p_y_x(i,k) = nchoosek(n,y(k)).*(x(i).^y(k)).*(1-x(i).^(n-y(k)));
    end
    index = find(p_y_x(i,:));
    p_y_x(i,index);
    
 h_y_x = [h_y_x -p_y_x(i,index)*log(p_y_x(i,index))'];
end

sec_term = x(n+1:2*n)*h_y_x';

q_y = p_y_x(i,index).*x(n+1:2*n);
first_term = q_y*log(q_y)';
z =  first_term + sec_term;



end

Answer 1

[Matt J]

There are no feasible solutions to your problem because it is impossible to satisfy the first equality constraint,

zeros(1,length(x))*x(:)=1

The left hand side will always be zero for every x.

[Manjunath Mulinti]

these are my constriants

could please suggest the changes i need to make in codeto satisfy above constraits

[Matt J]

What are the the knowns/unknowns?

[Manjunath Mulinti]

my knowns are q_y,h_y_x

unknowns are x0

we have find exact mass point location and probabilty by minimizing z

[Matt J]

unknowns are x0

I don't see any x0 in what you posted...

[Manjunath Mulinti]

we are giving x0 as x0 = [X0,p0];

where

X0 = rand(1,N);

p0 = ones(1,N) / N;

my aim is to minimize the objective function such that i get the exact mass ponts and their probalilites

[Matt J]

No, I'm asking about your problem definition. You said, about the equations you posted a few comments ago, that your unknows were "x0", but I don't see any x0 in the equations.

[Manjunath Mulinti]

we know x0 also we want minimize the objective function with x