Nonconvex Optimization

Nonconvex optimization tackles the challenge of finding optimal solutions in scenarios where the objective function possesses multiple local minima, hindering straightforward approaches. Current research emphasizes developing efficient algorithms, such as gradient descent variants (including those with momentum and adaptive learning rates), zeroth-order methods for gradient-free scenarios, and techniques leveraging block coordinate descent or sketching for scalability in high-dimensional problems. These advancements are crucial for addressing numerous applications across machine learning (e.g., training neural networks, robust matrix completion), signal processing, and network analysis, where nonconvex formulations frequently arise. The development of robust and efficient methods for escaping saddle points and achieving global or near-global optima remains a central focus.