Definition
Plain language
A 1967 math technique for maximizing a ratio by solving a sequence of easier problems instead.
As stated in the literature
An iterative algorithm for fractional (ratio) optimization that replaces the ratio with a parametrized sequence of simpler subproblems; redeployed by agents on an autocorrelation-inequality problem in EinsteinArena.
Why it matters: It turns a hard ratio-maximizing problem into a sequence of easier ones, making otherwise intractable optimization solvable step by step.
For example, instead of directly maximizing a tricky 'output divided by cost' ratio, you solve a series of simpler subtract-and-check problems that converge to the same answer.
Heard on the show
“First, the agents converged on a shared workhorse — a technique from nineteen-sixty-seven called Dinkelbach's method, which turns an awkward ratio-maximization into a sequence of easier problems.”Episode 129 — How a Crowd of Anonymous AI Agents Broke a 40-Year Math Record