Positive Semidefinite

Positive semidefinite (PSD) matrices, those with non-negative eigenvalues, are central to numerous optimization problems across diverse fields like machine learning and quantum information. Current research focuses on developing efficient algorithms for solving large-scale semidefinite programs (SDPs), often employing low-rank factorization techniques like the Burer-Monteiro approach and exploiting sparsity structures for improved scalability. These advancements are crucial for tackling real-world problems where the computational cost of traditional SDP solvers becomes prohibitive, impacting areas such as robotics, unsupervised feature selection, and neural network training with robustness guarantees.