Convex Approximation

Convex approximation focuses on replacing complex, non-convex problems with simpler, convex counterparts to facilitate efficient computation and analysis. Current research explores various techniques, including higher-order Newton methods, input-convex neural networks, and tailored convex polygon approximations of probabilistic reachable sets, often leveraging optimization algorithms like semidefinite programming or mixed-integer nonlinear programming. These advancements improve the speed and scalability of solving challenging problems across diverse fields, such as power systems optimization, robust control, and machine learning, where non-convexity often hinders practical application. The resulting gains in computational efficiency and solution quality are significant for both theoretical understanding and real-world deployment.