Decentralized methods for computing optimal real and reactive power setpoints for residential photovoltaic (PV) inverters are developed in this paper. It is known that conventional PV inverter controllers, which are designed to extract maximum power at unity power factor, cannot address secondary performance objectives such as voltage regulation and network loss minimization. Optimal power flow techniques can be utilized to select which inverters will provide ancillary services and to compute their optimal real and reactive power setpoints according to well-defined performance criteria and economic objectives. Lever-aging advances in sparsity-promoting regularization techniques and semidefinite relaxation, this paper shows how such problems can be solved with reduced computational burden and optimality guarantees. To enable large-scale implementation, a novel algorithmic framework is introduced-based on the so-called alternating direction method of multipliers-by which optimal power flow-type problems in this setting can be systematically decomposed into subproblems that can be solved in a decentralized fashion by the utility and customer-owned PV systems with limited exchanges of information. Since the computational burden is shared among multiple devices and the requirement of all-to-all communication can be circumvented, the proposed optimization approach scales favorably to large distribution networks.