A new perspective on low-rank optimization

Abstract A key question in many low-rank problems throughout optimization, machine learning, and statistics is to characterize the convex hulls of simple sets judiciously apply these obtain strong yet computationally tractable relaxations. We invoke matrix perspective function—the analog function—to explicitly hull epigraphs functions under constraints. Further, we combine function with orthogonal projection matrices—the binary variables which capture row-space a matrix—to develop reformulation technique that reliably obtains relaxations for variety problems, including reduced rank regression, non-negative factorization, factor analysis. Moreover, establish can be modeled via semidefinite constraints thus optimized over tractably. The proposed approach parallels generalizes mixed-integer optimization leads new broad class problems.