Results 1 to 1 of 1

Math Help - Minimise the Maximum Value

  1. #1
    Newbie
    Joined
    Oct 2007
    Posts
    11

    Minimise the Maximum Value

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

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

    Am I looking in the correct area? Can someone point the way forward please.
    Last edited by Mark@Work; October 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: November 10th 2010, 10:33 PM
  2. Replies: 3
    Last Post: December 9th 2009, 03:16 PM
  3. Can you help me minimise this function?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 19th 2009, 05:28 PM
  4. minimise maximise problem
    Posted in the Calculus Forum
    Replies: 9
    Last Post: February 26th 2009, 06:43 AM
  5. Minimise Radius- With a Nasty Twist.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: January 18th 2008, 06:36 AM

Search Tags


/mathhelpforum @mathhelpforum