I have an optimization problem where I have to optimize a function f(A) where A is a matrix(sparse).
Like
A = \begin{array}{cccc} A_1 & A_0 & A_0 & 0 \\ A_0 & A_2 & 0 & A_0 \\ A_0 & 0 & A_3 & A_0 \\ 0 & A_0 & A_0 & A_4 \\ \end{array}
A is a positive definite matrix and the variables are $A_i$. I want to optimize over these variables with the constraint that the matrix A is positive definite. Are there any softwares to help me out with this?
The CVX software package for MATLAB can handle semidefinite prodramming problems (SDPs).