  We show that the global minimum solution of $\lVert A - BXC \rVert$ can be
found in closed-form with singular value decompositions and generalized
singular value decompositions for a variety of constraints on $X$ involving
rank, norm, symmetry, two-sided product, and prescribed eigenvalue. This
extends the solution of Friedland--Torokhti for the generalized
rank-constrained approximation problem to other constraints as well as provides
an alternative solution for rank constraint in terms of singular value
decompositions. For more complicated constraints on $X$ involving structures
such as Toeplitz, Hankel, circulant, nonnegativity, stochasticity, positive
semidefiniteness, prescribed eigenvector, etc, we prove that a simple iterative
method is linearly and globally convergent to the global minimum solution.
