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

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Discussion Overview

The discussion revolves around the challenges of finding the domain of a discretized function for the purpose of minimization. Participants explore the nature of the function, its continuity, and the implications for optimization methods, particularly in the context of programming with Mathematica.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes a function that computes elliptic integrals and matrices, questioning whether it can be classified as a discretized function.
  • Another participant inquires about the order of magnitude of the domain's finiteness, suggesting a range from tens to millions.
  • The original poster clarifies that the function typically exists within a range of −1 to 4, but sometimes extends to 0 to 6 or other values.
  • A participant challenges the notion of the domain being finite, suggesting that the function may be discontinuous instead.
  • The original poster expresses uncertainty about the exact boundaries of the function's domain, indicating it is based on trial and error.
  • Another participant asks for clarification on the function's continuity and types of discontinuities present, such as jump or point discontinuities.
  • The original poster asserts that the function is continuous everywhere except for its limited domain and questions the definition of discontinuity.
  • Concerns are raised about the feasibility of evaluating the function at small intervals to determine its domain, given the long computation time of approximately 30 seconds per evaluation.
  • A request is made for the mathematical expression of the function to provide better assistance.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the function's domain and continuity. There is no consensus on how to define the function's characteristics or the best approach to find its domain for minimization.

Contextual Notes

Participants note limitations in the clarity of terminology and the need for more specific details about the function to facilitate discussion. The computational constraints of evaluating the function at small intervals are also highlighted.

noon0788
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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 :-p)

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!
 
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What order of magnitude of finiteness of the domain are we talking about here?
In the tens? Hundreds? Millions? Zillions?
 
It's about 5 wide.

Edit: I'd like to know the boundary within a reasonable accuracy. About 0.00001 or better.
 
5 wide means??
 
A domain of five. 5.0. The function usually exists from −1 to 4.
 
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
 
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.
 
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? :eek: 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?)
 
Last edited:
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...
 
  • #10
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.
 

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