We investigate a general optimization problem with a linear objective in which the coefficients are uncertain and the uncertainty is represented by a belief function. We consider five common criteria to compare solutions in this setting: generalized Hurwicz, strong dominance, weak dominance, maximality and E-admissibility. We provide characterizations for the non-dominated solutions with respect to these criteria when the focal sets of the belief function are Cartesian products of compact sets. These characterizations correspond to established concepts in optimization. They make it possible to find non-dominated solutions by solving known variants of the deterministic version of the optimization problem or even, in some cases, simply by solving the deterministic version.