Calculate minimum distance between point and steady but NON differentiable function
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I could not find any mathematical explanation regarding this topic on the internet and hope for your help. Is there a way to determine the minimum between a point P and a piecewise function, e.g.
A = piecewise(964<=x<=5007,((2450-10)/(5007-964))*(x-964)+10,x>5007,2450);
P = [4900;3000]
For a straight line this is normally done by finding the vertical to the envelope. But how does it look for a NON differentiable function? Is there only an iterative solution?Thanks for your help!
infinity on 12 Jul 2019
There is two options that you can think
Assume we have a point P(xp, yp) and a function f(x) that we may not have derivative. Then,
1. we can define a distant between P and f by
Now, what we have to do is to find the minimum of d(x).
There are several approaches in Matlab can help you find the minimum of d.
2. We can split piecewise function into several intervals such that in each interval the function has derivative and we can find distance from P to each line and also at the intersection. Then, we can compare these solution to find the global minimum.