This paper investigates a singular stochastic control problem for a
multi-dimensional regime-switching diffusion process confined in an unbounded
domain. The objective is to maximize the total expected discounted rewards from
exerting the singular control. Such a formulation stems from application areas
such as optimal harvesting multiple species and optimal dividends payments
schemes in random environments. With the aid of weak dynamic programming
principle and an exponential transformation, we characterize the value function
to be the unique constrained viscosity solution of a certain system of coupled
nonlinear quasi-variational inequalities. Several examples are analyzed in
details to demonstrate the main results