Finding mimum of a function with 2 local mins

In summary, the function is non-analytic and requires the use of the steepest descent method with numerical gradients to find the minimum. However, the location of the minimum depends on the starting point, with the left side resulting in a minimum on the left and the right side resulting in a minimum on the right. To consistently find the lowest point, it is necessary to know the location of the tall peak beforehand. An image of the function has been provided for better understanding.
  • #1
daviddoria
97
0
I have a function that looks like this:
http://rpi.edu/~doriad/view1.jpg The function is non analytic, so I have to use something like the steepest descent method with numerical gradients to find the minimum. However, if my starting point is on the left of the tall peak, the min I find is on the left side (clearly) and if I choose the starting point to be on the right side I find the low point on the right. Clearly in this case I could just do both and take the smaller one, but if I'm not sure about the location of the tall peak to start with, I can't simply choose a starting point on either side. Is there a way to find the actual lowest point consistently?

Thanks,

David
 
Last edited by a moderator:
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  • #2
Hi David,

I think it would be a lot better if you could provide an image of the function to make it all much more clear.
 
  • #3
The image has been posted.
Bump!
 

1. How do you determine the minimum of a function with 2 local mins?

To determine the minimum of a function with 2 local mins, you must first find the critical points of the function by taking the derivative and setting it equal to 0. Then, you can use the second derivative test to determine which critical point is the minimum.

2. Can a function have more than 2 local mins?

Yes, a function can have more than 2 local mins. In fact, a function can have an infinite number of local mins if it is a periodic function.

3. What is the difference between a local min and a global min?

A local min is a point on a function where the value of the function is lower than all points in the surrounding area. A global min is the lowest value of the function for the entire domain.

4. How can you graphically identify the local mins of a function?

You can graphically identify the local mins of a function by looking for points on the graph where the slope changes from negative to positive. These points represent the local mins of the function.

5. Can a function have 0 local mins?

Yes, a function can have 0 local mins. This can happen if the function is strictly increasing or strictly decreasing over the entire domain.

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