Non Convex

Non-convex optimization tackles the challenge of finding optimal solutions in mathematical landscapes with multiple local minima, hindering straightforward approaches like gradient descent. Current research focuses on developing efficient algorithms, such as variations of stochastic gradient descent, augmented Lagrangian methods, and Newton-like methods, often tailored to specific problem structures (e.g., low-rank matrices, tensor completion, or neural networks). These advancements are crucial for solving complex problems in machine learning, robotics, and signal processing, where non-convexity is inherent, enabling improved model performance and reduced computational costs. The development of robust and scalable methods for non-convex problems remains a significant area of ongoing investigation.