Over the last few years, there has been a significant shift in the design and operation of radio access networks from coverage and capacity optimization to energy efficiency. This paper presents a novel algorithm that exploits the redundancy in a multi radio access technology (multi-RAT) network based on UMTS and LTE technologies to reduce the overall energy consumption. The energy-efficiency gains are achieved by reconfiguring the network so as to find a set of active network components that consumes the least amount of energy and that is necessary to provide the quality of service required by the users. The problem is formulated as an integer programming problem, the solution of which shows the components that should be active in order to minimize the energy consumption. Since the problem is intractable for large networks, we relax the initial problem and apply techniques successfully used in, for example, sparse signal reconstruction or statistical estimation. The resulting relaxed problem is solved by means of majorization-minimization methods to obtain algorithmic solutions leading to a low total energy consumption. The potential of the proposed approach for huge energy savings in multi-RAT environments is demonstrated in a dynamic simulation setup.