Optimization of an objective given as a ratio, such as area divided by perimeter. When the denominator is positive, a trial ratio can be tested by maximizing numerator minus times denominator.
For maximizing with , repeatedly maximize and update to the ratio at the selected maximizer. If the maximum difference is zero, is the optimal ratio. Exact convergence claims require the relevant existence and regularity assumptions.
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Fractional programming is a type of mathematical optimization that involves optimizing a fractional objective function, where the objective function is defined as the ratio of two functions. Typically, these functions are continuous and may be either linear or nonlinear.