Werner Dinkelbach

Werner Dinkelbach developed a method for nonlinear fractional programming. Instead of directly optimizing a ratio $f(x)/g(x)$ with positive denominator, the method repeatedly optimizes $f(x)-\lambda g(x)$ and updates $\lambda$ from the resulting ratio. The transformation connects the optimal ratio with a zero of a scalar value function, giving the ratio problem a sequence of simpler parametric subproblems.^[ref]