For over three centuries, researchers have relied on a powerful algorithm developed by Isaac Newton to tackle complex problems in logistics, finance, computer vision, and even pure math. This simple yet effective method provides a remarkable way to approximate solutions when direct calculations are too complex. But even a method devised by one of history’s greatest minds has its limitations — it doesn’t work well on all functions. A team of researchers has now expanded Newton’s method, making it more powerful than ever. Most recently, Yurii Nesterov of Corvinus University of Budapest developed a method in 2021 that could handle multiple variables using cubic equations. However, extending it to more complex equations, like quartic or quintic, made it inefficient. Ahmadi, Chaudhry, and Zhang have built on Nesterov’s work to develop an algorithm that handles any number of variables and derivatives while staying efficient—something that was previously thought impossible.
More details are inside the link... The report was published in March 2025. The technical paper itself is from 2023:
https://arxiv.org/abs/2311.06374