Here is an animation of how the function minimizer Minuit minimizes a function. The function to be minimized depends on two parameters so that one can visualize it. It was inspired by the ‘banana shaped valley’ function so that Minuit must take several steps to find the minimum. The value of the goal function is indicated by the color, i.e. the goal function is a ‘spiral’ whose depth increases as one goes more counterclockwise.
The types of the steps (shown at the top left) were inferred from the functions from which it was called. The minimization typically has two alternating phases: numerical determination of the gradient and line search along some promising direction. At the end, the second derivative is calculated (although the function has a discontinuity on one side).
The red point shows the coordinates with which Minuit calls a goal function to be minimized.
The arrow at the top left shows the direction from the previous to the current step. For example during the line search phase, the direction remains mostly fixed or is reversed while during the gradient calculation phase it looks like first the horizontal component is calculated and then the vertical one.
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