The Method of Steepest Descent, also known as the Gradient Descent method, is an optimization technique used to find the minimum of a function. The core idea behind this method is to iteratively move toward the direction of steepest descent, which is indicated by the negative gradient of the function.
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A contour integral with a large exponential parameter is deformed through saddle points along curves on which the real part of the phase decreases most rapidly and the imaginary part is locally constant.