Given a simple generic optimization problem
argmin y = (A+B)x + g(x) + epsilon
Let's say we want to fix the matrix A, and allow for free-form optimization on B. What kind of regularization or constraints can we simply impose on B in such way that elements of B will not cancel out the elements of the fixed matrix A?
Edit: Let us also further assume that matrix A is generally sparse, i.e. we want to include some prior knowledge of (A+B) in this problem by providing the known matrix A. My concern is that in many cases, some elements of A will be canceled out by B.
Edit2: Maybe we can even relax this constraint further. We do not want to completely prevent B from canceling out A, but simply want to encourage B to not do so.