A method for adapting the regularization parameter of weak continuity

We invoke a basic lemma from the theory of so-called penalty methods of nonlinear programming to come up with a simple yet highly efficient block-adaptive training procedure that selects a suitable weak continuity (WC) regularization parameter by matching the complexity ("prior") of the resulting solution to that of a desired response. The matching is achieved using a simple binary search technique that is guaranteed to converge in very few steps; as such, it avoids many of the potential pitfalls of other iterative methods.