Optimization Inverse Spectral Problem for the One-Dimensional Schrödinger Operator on the Entire Real Line

We study the statement of the optimization inverse spectral problem with incompletespectral data for the one-dimensional Schrödinger operator on the entire axis: for a givenpotential \(q_0\) , find the closest function \(\hat {q}\) such that the first \(m\) eigenvalues of the Schrödinger operatorwith potential \(\hat{q}\) coincide with given values \(\lambda _k^*\in \mathbb {R}\) , \(k={1,\dots ,m}\) .