We present a shape manipulation technique capable of producing deformations of 2D and 3D meshes, guaranteeing that no elements will be inverted. We achieve this by augmenting the quadratic ex‐rotated elastic energy with additional convex terms that penalize the presence of inverted elements. Using a schedule of increasing penalty coefficients, we efficiently and robustly converge to an inversion free state by solving a sequence of unconstrained convex minimization problems. This process can be interpreted as a special purpose Semi‐Definite Programming (SDP) solver. We demonstrate that our method outperforms solvers used in previous work, including commercial‐grade SDP software (MOSEK). As an additional benefit, our method also converges to the solution via a more intuitive path, which can be used for quick preview. We demonstrate the efficacy of our scheme in a number of 2D and 3D shapes undergoing moderate to drastic deformation.