Conventional energy generation sources mainly provide energy supply to remote areas nowadays. However, because of growing concerns over greenhouse gas emissions, the integration of renewable energy sources is mandatory to meet power demands and reduce climatic effects. The advancements in renewable generation sources and battery storage systems pave the way for microgrids (MGs). As a result, MGs are becoming a viable solution for power supply shortage problems in remote-area applications, such as oceanic islands. In this paper, an islanded MG, which consists of PV system, tidal turbine (TT), diesel generator (DG), and Li-ion battery, is considered for Ouessant island in Brittany region in France. The economic operation of the MG is achieved by including battery degradation cost, levelized costs of energy of the PV system and TT, operating and emission costs of DG, and network constraints. The developed model leads to a non-linear and non-convex problem, which unfortunately can converge to a local optimum solution. The problem has, therefore, been relaxed and converted to a convex second-order cone model to achieve an optimal decision strategy for islanded MG operations with a global or near-global solution. Numerical simulations are carried out to prove the effectiveness of the proposed strategy in reducing the operating and emission costs of the islanded MG. It is shown that the developed convex energy management system formulation has an optimality gap of less than 1% with reduced computational cost.