Researchers continue to search for optimal solutions daily in various fields such as transportation, finance, and technology. Finding the minimum values of complex functions is a daunting task, but Isaac Newton’s centuries-old algorithm remains crucial for this endeavor. Mathematicians have worked to extend and improve Newton’s method over time. Last summer, Amir Ali Ahmadi and his colleagues announced a breakthrough with an algorithm that efficiently works on the broadest class of functions yet, surpassing Newton’s original method. By utilizing semidefinite programming, they tweaked the Taylor approximations to make the equations convex and a sum of squares, leading to faster convergence towards the true minimum value.
https://www.quantamagazine.org/three-hundred-years-later-a-tool-from-isaac-newton-gets-an-update-20250324/