Generalized Geometry Block Proximal Linearized Method for Multiblock Nonconvex and Nonsmooth Optimization

Excerpt

arXiv:2609.39301v1 Announce Type: cross Abstract: This paper considers a class of multiblock nonconvex and nonsmooth optimization problems arising in many applications. Existing methods construct proximal linearized operators or their variants within standard Euclidean geometry to solve this class of problems, forcing their block variable updates to rely on the standard inner product and its induced norm. Nevertheless, this construction fails to capture the geometric structure of the target prob