This paper addresses the problem of coordinated beamforming across a group of base stations (BSs) and frequency slots in the downlink of a multiple-input multiple-output (MIMO) orthogonal frequency-division multiple-access (OFDMA) cellular network. Three figures of merit are considered for system design under a per-BS power constraint: 1) the weighted sum of the rates (WSR) on the frequency slots of the coordinated BSs; 2) the global energy efficiency (GEE), defined as the ratio between the network sum rate and the corresponding consumed power; and 3) the weighted sum of the energy efficiencies (WSEE) on the frequency slots of the coordinated BSs. The Karush–Kuhn–Tucker (KKT) conditions of the considered optimization problems are first derived to gain insight into the structure of the optimal beamformers. Then, we propose a suboptimal design method that can be applied to all considered figures of merit. Numerical results are provided to assess the performance of the proposed beamforming strategies.