MORE@DIAG: Adrian Lewis (Cornell) Identifiability, Nonconvexity, and Sparse Optimization Algorithms
The notion of "identifiability" underpins the active-set philosophy in optimization, and often manifests itself in variational formulations seeking low-dimensional structure from high-dimensional data. Beyond the realm of convexity, identifiability remains a fundamental property, occurring generically in semi-algebraic optimization. I illustrate its relevance for two simple and popular nonconvex algorithms: alternating projections and a proximal algorithm for composite optimization.
Joint work with J. Bolte, A. Daniilidis, D. Drusvyatskiy and S. Wright