optimization - How to find and/or optimize the best set of parameter values of a function to create specific curve given a set of conditions in R

Question

The overall goal is to get a function which returns a percentage (Y) subject to a quantity (X). I want to know if there is any way I can do this in R. I know I want the function to be s-shaped like so:

Yielding a set of percentages (Y) given corresponding quantities (X):

This means I have a the given set of parameters which affect how this curve is shaped:

• min
• max
• X0
• a
• k

I would like to set the minimum and maximum Y values myself. X0, a and k I would like to somehow automatically optimize to yield the exact shape that I want given a set of conditions.

These conditions are of the form:

1. When can the curve start to grow, e.g. departure from minimum value can start at x = 30,000
2. When X = (something) Y needs to be (something)
3. If possible some form of condition specifying relative growth rates/differences, e.g. between X = 30,000 and X = 60,000 the difference in Y must be (something)

Generally, I am asking if there is some programmatic way of getting the curve I want, instead of me having to sit and experiment manually with these parameter values in excel.

I hope this makes sense, and that someone can help. Thank you in advance!

Answer 1

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