Multiparametric MRI registration between pre- and postoperative brain scans, which is the subject of the BraTS-Reg Challenge, poses a complex problem to solve due to large deformations and missing correspondences. We make use of hand-crafted geometric features, coupled convex optimisation, and an Adam-based instance optimisation. Our method only requires few trainable parameters and is able to perform accurate image alignment while using smooth and plausible deformation fields. For our challenge submission, we achieved a mean median target registration error of 1.77 mm on the validation dataset. ConvexAdam ranks 2nd both in the ISBI-2022 and MICCAI-2022 BraTS-Reg Challenge.