Results 1 to 2 of 2

Math Help - Converting function to Quadratic form

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    6

    Converting function to Quadratic form

    Hi everyone. I'm looking for help with converting this function to quadratic form.

    The function is f(x1,x2)=(x2-x1)^4 + (12*x1*x2) - x1 + x2 - 3.

    The quadratic form I need to convert to is: f(x)=(1/2)x'Qx - x'b + h

    where x is a vector=[x1 x2]', '=transpose, Q and b are vectors, and h is the constant. Also, Q is symmetric and positive definite (Q=Q' > 0).

    The trouble I'm running into is that f(x1,x2) is 4th order, and the examples I have convert only 2nd order functions to the f(x) quadratic objective format above.

    In case your interested, I'm looking for this info to solve a steepest descent problem, where the varying ak value is ak=g(k)'g((k))/( g(k)'Qg(k) ) where g(k)=Qx(k) - b.

    Thanks in advance!
    Last edited by scg4d; February 13th 2010 at 03:13 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,447
    Thanks
    1863
    Quote Originally Posted by scg4d View Post
    Hi everyone. I'm looking for help with converting this function to quadratic form.

    The function is f(x1,x2)=(x2-x1)^4 + (12*x1*x2) - x1 + x2 - 3.

    The quadratic form I need to convert to is: f(x)=(1/2)x'Qx - x'b + h

    where x is a vector=[x1 x2]', '=transpose, Q and b are vectors, and h is the constant. Also, Q is symmetric and positive definite (Q=Q' > 0).

    The trouble I'm running into is that f(x1,x2) is 4th order, and the examples I have convert only 2nd order functions to the f(x) quadratic objective format above.
    Well, yes. That's because 2nd order functions are quadratic! You cannot write a function that is NOT quadratic in a quadratic format.

    In case your interested, I'm looking for this info to solve a steepest descent problem, where the varying ak value is ak=g(k)'g((k))/( g(k)'Qg(k) ) where g(k)=Qx(k) - b.

    Thanks in advance!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. quadratic function standard form
    Posted in the Algebra Forum
    Replies: 3
    Last Post: March 10th 2010, 02:59 AM
  2. Replies: 2
    Last Post: March 9th 2010, 09:33 PM
  3. Converting to Q = ae^kt form
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: March 1st 2010, 05:30 PM
  4. Converting from Polar form to Rectangular form
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 26th 2009, 11:47 PM
  5. Replies: 1
    Last Post: June 12th 2008, 10:30 PM

Search Tags


/mathhelpforum @mathhelpforum