Is it Possible to Find the Domain of a Discretized Function for Minimization?

[noon0788]

Hello! I'm not quite sure where to put this. I'm programming, but my question should be strictly mathematical. However, just for your information, I'm programming with Mathematica.

I have a function that will give me points. If I give it inputs, I can get a value out of it. I can take a bunch of points and smooth it out to get a curve, but I can't get a continuous curve because internally, the function is computing elliptic integrals and matrices. Would this be considered a discritized function then? Am I in the realm of discrete mathematics? (I sure hope not )

Anyway, I need to minimize said function. I have a gradient search method that will find the minimum in certain cases, but because the domain of the function is finite, I'm sometimes ending up searching outside the domain and the minimization fails. If there's some way to find the domain of this "discritized" function, perhaps I could constrain the minimization.

Can anybody guide me on this? Even a nudge in the direction of a good resource would be quite helpful. Thanks!

 

[arildno]

What order of magnitude of finiteness of the domain are we talking about here?
In the tens? Hundreds? Millions? Zillions?

 

[noon0788]

It's about 5 wide.

Edit: I'd like to know the boundary within a reasonable accuracy. About 0.00001 or better.

 

[arildno]

5 wide means??

 

[noon0788]

A domain of five. 5.0. The function usually exists from −1 to 4.

 

[Office_Shredder]

So your domain is not actually finite?

I think you need to give a few more details about what's going on. It sounds from your post like you just have a discontinuous function

 

[noon0788]

Ok, I'm sorry. I guess I wasn't clear or my understanding of the terminology is wrong. I don't know what the domain of the function is, but it usually ranges from −1 to 4. Sometimes it's 0 to 6. Other times, it seems to be 0 to 4.2763649... I don't know what its boundaries are. These are all rough guesses after trial and error. The domain is finite in the sense that it doesn't go on forever, but I don't know what it is. And yes, it is discontinuous.

 

[Office_Shredder]

So from what I gather there is some parameter that changes what the function is, and you want to find the minimum of the function for different values of this parameter?

How discontinuous is your function? Continuous almost everywhere? Continuous in most places? Continuous nowhere? Jump discontinuities, point discontinuities, asymptotes?

I would be very surprised if there was an algorithm that could just take a function and tell you what its domain is, outside of just plugging in numbers with very small intervals and seeing if the function evaluates (why is this not viable? Does it take too long to evaluate the function?)

 

[noon0788]

It's continuous everywhere except for it's limited domain. There are no jumps or steps. I thought that a function was considered to be discontinuous if it abruptly cut off. It doesn't asymptote or converge; it just cuts off. Am I wrong to say that it's discontinuous?

And you're right Shredder, the function takes about 30 seconds to evaluate. Plugging in numbers with small intervals just wouldn't be an option for me...

 

[arildno]

Give us the expression for the function you are asking about.
You are far too vague and unclear in your terminology you offer us any assistance whatsoever.