Nonconvexity Setting

Nonconvexity in optimization poses significant challenges across diverse fields, from machine learning to computer vision, as many real-world problems lack the convenient properties of convexity. Current research focuses on understanding the impact of nonconvexity on algorithm performance, particularly investigating the convergence properties of first-order methods like stochastic gradient descent and exploring techniques like smoothing and cohypomonotonicity to mitigate its effects. This work is crucial for developing robust and efficient algorithms for solving complex problems in various applications, including generative modeling, risk-constrained learning, and process optimization, where nonconvexity is inherent. The ultimate goal is to develop a deeper theoretical understanding of nonconvex optimization landscapes and design algorithms that reliably find global or near-global optima.