This paper presents a global mesh optimization framework for 3D triangular meshes of arbitrary topology. The mesh optimization task is formulated as an energy minimization problem including data attached terms measuring the fidelity to the original mesh as well as a shape potential favoring high quality triangles. Since the best solution for vertex relocation is strongly related to the mesh connectivity, our approach iteratively modifies this connectivity (edge and vertex addition/removal) as well as the vertex positions. Good solutions for the energy function minimization are obtained by a discrete graph cut algorithm examining global combinations of local candidates. Results on various 3D meshes compare favorably to recent state-of-the-art algorithms regarding the trade-off between triangle shape improvement and surface fidelity. Applications of this work mainly consist in regularizing meshes for numerical simulations, for improving mesh rendering or for improving the geometric prediction in mesh compression techniques.