  Following ideas from the Abstract Interpolation Problem of Katsnelson et al.
(Operators in spaces of functions and problems in function theory, vol 146, pp
83-69, Naukova Dumka, Keiv, 1987) for Schur class functions, we study a general
metric constrained interpolation problem for functions from a vector-valued de
Branges-Rovnyak space $\mathcal{H}(K_S)$ associated with an operator-valued
Schur class function $S$. A description of all solutions is obtained in terms
of functions from an associated de Branges-Rovnyak space satisfying only a
bound on the de Branges-Rovnyak-space norm. Attention is also paid to the case
that the map which provides this description is injective. The interpolation
problem studied here contains as particular cases (1) the vector-valued version
of the interpolation problem with operator argument considered recently in Ball
et al. (Proc Am Math Soc 139(2), 609-618, 2011) (for the nondegenerate and
scalar-valued case) and (2) a boundary interpolation problem in
$\mathcal{H}(K_S)$. In addition, we discuss connections with results on kernels
of Toeplitz operators and nearly invariant subspaces of the backward shift
operator.
