Orthogonality Constraint

Orthogonality constraints, requiring solutions to maintain specific geometric relationships (e.g., orthogonality of matrices), are central to many optimization problems in machine learning and scientific computing. Current research focuses on developing efficient algorithms, such as retraction-free methods and block coordinate descent, to address the computational challenges posed by these constraints, particularly in high-dimensional settings and decentralized environments. These advancements are improving the performance and scalability of various applications, including cross-lingual embedding, feature selection, and robust neural network training, by enabling more effective optimization within constrained solution spaces. The development of more efficient and robust algorithms for handling orthogonality constraints is crucial for advancing numerous fields relying on large-scale data analysis and complex model training.