Optimization on the Oblique Manifold for Sparse Simplex Constraints via Multiplicative Updates

ArXi:2503.24075v3 Announce Type: replace-cross Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-1 conditions, making their optimization particularly challenging due to the interplay between low-rank structures and constraints. These problems arise in various applications, including machine learning, signal processing, environmental fields, and computational biology. In this work, we propose a novel manifold optimization approach to efficiently tackle these problems.