How to represent this set of positive semidefinite matrices into a cvx variable?

[Mark_L_Stone]

it should work for any number of dimensions.

How to change the number of variables based on the iteration number?

Why not use multidimensional arrays? For instance: variable Q_1(n,n,k) hermitian; variable Q_2(n-1,n-1,k) hermitian; Then you can access an individual ‘slice’ with colon notation; e.g., Q_1(:,:,k). From the documentation: Matrix-specific keywords can be applied to n-dimensional arrays as well: each 2-dimensional “slice” of the array is given the stated structure. So for instance, the declaration variable R(10,10,8) hermitian semidefinite constructs 8 10×10 complex Hermitian PSD matr…