Projection Free

Projection-free methods in optimization aim to solve constrained optimization problems without explicitly projecting onto the feasible set, thus avoiding computationally expensive projection operations, particularly beneficial in high-dimensional spaces. Current research focuses on developing and analyzing projection-free algorithms based on techniques like Frank-Wolfe, conditional gradient methods, and variance reduction, applied to diverse problem settings including online convex optimization, stochastic optimization, and bilevel optimization. These advancements offer significant improvements in computational efficiency and scalability for various applications, ranging from image editing and machine learning to control systems and resource allocation.