  This work concerns the distance in 2-norm from a matrix polynomial to a
nearest polynomial with a specified number of its eigenvalues at specified
locations in the complex plane. Perturbations are allowed only on the constant
coefficient matrix. Singular value optimization formulas are derived for these
distances facilitating their computation. The singular value optimization
problems, when the number of specified eigenvalues is small, can be solved
numerically by exploiting the Lipschitzness and piece-wise analyticity of the
singular values with respect to the parameters.
