Prox is not working. X(:, i+1) is not well defined. When I put X = rand(10,1) and prox_L1(X, 0.5) then it's working. But I am not getting X(:, i+1). I want to run the followin

n = 10;

p=1;

A= rand(n);

A= 0.5*(A'+ A);

i=1;

X(:,i)=rand(n,p);

lambd3(i) = 1/3;

mu = 0.9;

for i = 1:100

a_i = 1/(i+1)^0.5;

L=(norm(A))^2;

beta= abs(min(eig(A)));

s_i=2*beta/L;

gamma_i = 0.005*s_i;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5

%%Alg1

f_i = -2*X(:,i)'*A'*A;

%2*A'*A*X(:,:,i) - 2*A'*B;

Z_i = X(:,i) - s_i*(f_i);

Y_i = prox_L1(Z_i,gamma_i);

X(:,i+1) = Y_i;

L(i) = norm(X(:,i+1) - X(:,i))

% n(i)=i;

end

n=[1:1:100];

plot(n,L(n),'color',[0.80 0 0], Marker='-.','LineWidth',2,'markersize',4);

[feeroz babu]

> n=10;

>> p=1;

>> X=rand(n,p);

>> prox_L1(X, 0.5)

ans =

0.386084092595876

0

0.150081811040748

0

0.330508755645148

0

0.495992461466452

0

0

0

>>

Answer 1

[Sriram Tadavarty]

Hi Feeroz,

Here are some of the inputs that I can provide without knowing how the prox_L1 code is.

The issue is that Z_i is a matrix of size 10 x 10, and this matrix is trying to fit to a vector X of size 10 x 1.

When the value of X(:,i) set to rand(n,p) gives a column vector of length 10, since p is 1. The matrix A is of size 10 x 10.

    f_i = -2*X(:,i)'*A'*A;     % Here f_i is of size 1 x 10 
    Z_i =  X(:,i) - s_i*(f_i); % Here Z_i is of size 10 x 10 
    % This Z_i is passed to prox_L1 function, which might return the output
    % with same dimensions thereby not able map to a vector of length 10.

When Z_i is of size 10 x 1, then the code would run as expected. So, updating f_i or Z_i could be a solution to avoid the issue.

Another aspect is to define X with zeros before accessing the elements, as it would make the code clear. Like, in this case X can be initialized to zeros(10,101). first input 10 is for n, second input 101 is to access all the i & i+1 values in the for loop.

Hope this helps.

Regards,

Sriram