Diving for Sparse Partially-Reflexive Generalized Inverses

Generalized inverses form a set of key tools in matrix algebra. For large-scale applications, sparsity is highly desirable, and so sparse generalized inverses have been studied. One such family is based on relaxing the well-known Moore-Penrose properties. One of those properties is non-linear, and so we develop a convex-programming relaxation and an associated “diving” heuristic to achieve a good trade-off between sparsity and satisfaction of the non-linear Moore-Penrose property.