A constrained approximation problem arising in parameter identification (Q1611917)

The following approximation problem arising in boundary parameter identification problems is considered: Given \(f\in L^2(I)\), \(\Psi\in L^2(J)\) and \(M\geq 0\), find \(g_2\in H^2\) such that \(\|\text{Im }g_2-\psi\|_J\leq M\) and \[ \|g_2-f\|=\min\{\|g-f\|_1\mid g\in H^2\text{ satisfying }\|\text{Im g}-\psi\|_J\leq M\}. \] The authors present a constructive algorithm and illustrate the method by a numerical example.