Results 1 to 1 of 1

Thread: Minimise the Maximum Value

  1. #1
    Oct 2007

    Minimise the Maximum Value

    I have two simple vector equations:
    $\displaystyle \vec{F_{T}}=\sum_{i=0}^n{\vec{F_{i}}}$
    $\displaystyle \vec{L_{T}}=\sum_{i=0}^n{\vec{F_{i}} \times \vec{H_{i}}}$ : ( $\displaystyle \times$ being the vector (aka cross) product).
    I know $\displaystyle \vec{F_{T}}$ , $\displaystyle \vec{L_{T}}$ and all values of $\displaystyle \vec{H_{i}}$. I want to find sensible values for the $\displaystyle \vec{F_{i}}$ .

    When n = 2 this is a simple simultaneous equation.
    However when n > 2 there is no single point solution.
    Consider n=3; one could view the two equations as defining planes, the intersection of these planes would then define a line of points that satisfy the two equations.
    What I want is the solution from this range that minimises the largest value of $\displaystyle \vec{F_{i}}$.

    My current thinking is set all except 2 of the $\displaystyle \vec{F_{i}}$ to zero and solve the resulting simultaneous equation.
    Repeat for a different pair of $\displaystyle \vec{F_{i}}$
    This gives two points on the solution line.
    Find the perpendicular to this line that passes through the origin (All $\displaystyle \vec{F_{i}}=0$)

    Am I looking in the correct area? Can someone point the way forward please.
    Last edited by Mark@Work; Oct 24th 2007 at 08:04 AM. Reason: Improved LaTex skills
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Minimise A= 1/2(1-x+qx^2)
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Nov 10th 2010, 10:33 PM
  2. Replies: 3
    Last Post: Dec 9th 2009, 03:16 PM
  3. Can you help me minimise this function?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Aug 19th 2009, 05:28 PM
  4. minimise maximise problem
    Posted in the Calculus Forum
    Replies: 9
    Last Post: Feb 26th 2009, 06:43 AM
  5. Minimise Radius- With a Nasty Twist.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Jan 18th 2008, 06:36 AM

Search Tags

/mathhelpforum @mathhelpforum