In this work, the design of gradient coils for magnetic resonance imaging (MRI) is studied as a multi-objective optimization (MOP) problem, which is successfully solved by using Pareto optimality formalism. The proposed approach is illustrated using a stream function inverse boundary element method (IBEM), as the coil design paradigm that is capable of including numerous design requirements or objectives. These are frequently in conflict, which stresses the need to deal efficiently with the tradeoff between different coil properties. It is shown that the inclusion of many of the most commonly used coil design requirements (such as field homogeneity, uniformity, magnetic stored energy, power dissipated, torque balanced ... ) reduces the problem to a convex MOP, where Pareto optimal solutions can be efficiently found by using suitable convex optimization procedures. Pertinent examples are studied to illustrate the versatility of the proposed MOP approach, which can be used to obtain a comprehensive understanding of the coil design problem, as well as to handle the different coil requirements efficiently and how they should be combined to yield the best solution for a given problem.