Projection Algorithm

Projection algorithms are mathematical methods used to find the closest point in a given set (e.g., a ball, a manifold, or a subspace) to a given point, often crucial for solving optimization problems. Current research focuses on improving the efficiency and scalability of these algorithms, particularly for high-dimensional data and non-convex problems, exploring techniques like variable projection, accelerated gradient methods, and unitary transformations within various architectures such as neural networks and tensor algebras. These advancements are impacting diverse fields, including machine learning (e.g., sparse autoencoders, bundle adjustment), signal processing, and scientific computing (e.g., solving partial differential equations), by enabling faster and more accurate solutions to complex problems.