Speaker: Deniz Akkaya
Time: July 5, 10:30
Meeting ID: 993 766 4491
Title: Minimizers of Sparsity Regularized Robust Loss Functions
Abstract: We look for the structure of the local and global minimizers of the Huber loss and the sum of absolute deviations functions regularized with a sparsity penalty l0 norm term. We characterize local minimizers for both loss functions and establish conditions that are necessary and sufficient for local minimizers to be strict. A necessary condition is established for global minimizers, as well as the non-emptiness of the set of global minimizers. The sparsity of minimizers is also studied by giving bounds on a regularization parameter controlling sparsity. Results are illustrated in numerical examples.