Results 1 to 6 of 6

Thread: Optmization Problem

  1. #1
    Newbie
    Joined
    Sep 2016
    From
    US
    Posts
    3

    Optmization Problem

    Determine the value of the constant k which best approximates a specified function f(x) on the interval 𝑎≤𝑥≤𝑏. Use as a cost function to be minimized:
    Optmization Problem-problem.png

    Verify that a minimum is achieved by checking the 2nd order optimality condition.


    I rewrote L(k) and then tried to find the value of k such that dL(k)/dk = 0. Am I allowed to simplify like this?
    Optmization Problem-work.png
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,362
    Thanks
    1667

    Re: Optmization Problem

    Hey Sylvan.

    You can write it like this but you should be careful in your algebra.

    The integral you evaluate as coefficients of your k^2 and k terms will not be the ones you got in your derivative term.

    You will need to evaluate these integrals and if the x and k variables are independent then they will become the proper coefficients just like d/dx ax^2 = 2ax and not 2x.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2016
    From
    US
    Posts
    3

    Re: Optmization Problem

    k is a constant, not a variable, which is why I pulled it out of the integral.

    I tried evaluating the integrals again:

    Optmization Problem-work2.png

    And I apologize for the double thread, this one didn't show up. I will try to delete the duplicate.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    18,576
    Thanks
    2590

    Re: Optmization Problem

    If you are asking "what value of k ..." then you must treat k as a variable! If it were a constant then it could have only one value.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,362
    Thanks
    1667

    Re: Optmization Problem

    Your working looks good.

    You should intuitively imagine that the function is a sort of "average" where you have a constant line through that average point to understand what is being described.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member Rebesques's Avatar
    Joined
    Jul 2005
    From
    My house.
    Posts
    655
    Thanks
    41

    Re: Optmization Problem

    Minor typo, since x^b_a=b-a, the answer should be k=\frac{f(b)-f(a)}{b-a}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. optmization - crossing river with moving water
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Oct 29th 2009, 10:11 AM
  2. [SOLVED] Optmization - Cost
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Apr 7th 2009, 05:21 PM

Search Tags


/mathhelpforum @mathhelpforum