It has recently been shown that several classical open problems in linear system theory, such as optimization of decentralized output feedback controllers, can be readily solved for positive systems using linear programming. In particular, optimal solutions can be verified for large-scale systems using computations that scale linearly with the number of interconnections. Hence two fundamental advantages are achieved compared to classical methods for multivariable control: Distributed implementations and scalable computations. This paper extends these ideas to the class of positively dominated systems. The results are illustrated by computation of optimal spring constants for a network of point-masses connected by springs.