Convex Problem

Convex optimization focuses on finding the minimum or maximum of a convex function, a problem with broad applications across science and engineering. Current research emphasizes developing efficient algorithms, particularly for large-scale problems and those involving constraints like sparsity or probability simplex restrictions, with a focus on methods like proximal gradient descent, ADMM, and accelerated variants. These advancements improve the speed and scalability of solving convex problems, impacting fields such as machine learning (e.g., neural network training), signal processing, and control systems by enabling more complex models and faster computations.