Modern optimization techniques in computer vision

This thesis presents research into multiple optimization topics in computer vision with a conceptual focus on composite optimization problems such as bilevel optimization. The optimal graph-based discretization of variational problems in minimal partitions, the theoretical analysis of nonconvex composite optimization by nonconvex majorizers, the bilevel problem of learning energy models by nonconvex majorizers, and the machine learning security applications of bilevel optimization in privacy analysis of federated learning and dataset poisoning of general image classification are featured in this cumulative work.