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Three Hundred Years Later, a Tool from Isaac Newton Gets an Update

A simple, widely used mathematical technique can finally be applied to boundlessly complex problems.

Although enormously powerful — centuries later, Newton’s method is still crucial for solving present-day problems in logistics, finance, computer vision and even pure math — it also has a significant shortcoming. Functions can have dozens of variables raised to high powers, defying formulaic analysis; graphs of their solutions form high-dimensional landscapes that are impossible to explore from a bird’s-eye view. But Ahmadi, Chaudhry and Zhang figured out how to use a technique called semidefinite programming to wiggle the Taylor approximation just enough to make it both a sum of squares and convex, though not so much that it became unmoored from the original function it was supposed to resemble.

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