  We consider optimization problems involving the multiplication of variable
matrices to be selected from a given family, which might be a discrete set, a
continuous set or a combination of both. Such nonlinear, and possibly discrete,
optimization problems arise in applications from biology and material science
among others, and are known to be NP-Hard for a special case of interest. We
analyze the underlying structure of such optimization problems for two
particular applications and, depending on the matrix family, obtain
compact-size mixed-integer linear or quadratically constrained quadratic
programming reformulations that can be solved via commercial solvers. Finally,
we present the results of our computational experiments, which demonstrate the
success of our approach compared to heuristic and enumeration methods
predominant in the literature.
