General Nonconvex

General nonconvex optimization focuses on finding optimal solutions for problems where the objective function lacks the convenient properties of convexity, posing significant computational challenges. Current research emphasizes developing efficient algorithms, such as variance-reduced gradient estimators, second-order methods tailored to specific nonconvex structures (e.g., sparsity-promoting regularizers), and momentum-based approaches, often within frameworks like stochastic gradient descent and its variants. These advancements are crucial for tackling complex problems in machine learning, including robust regression, minimax optimization, and differentially private learning, where nonconvexity is inherent. The resulting improvements in algorithm efficiency and theoretical guarantees are driving progress across numerous scientific and engineering disciplines.