Results 1 to 2 of 2

Math Help - Linear Programming

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    2

    Linear Programming

    Hi I have a question with regarding to a linear programming question.

    suppose the problem has a disk constraint of the form

    x^2+y^2<=1. this constraint is non linear and hence cannot b written in the form of AX<=b. for some finite matrix A and vector b. describe a construction of an infinite number of linear constraints on x such that the feasible set for all of these constraints together is equal to the disk.

    Your help will greatly appreciate.

    Thanks
    Jupiter
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by jupitertang View Post
    Hi I have a question with regarding to a linear programming question.

    suppose the problem has a disk constraint of the form

    x^2+y^2<=1. this constraint is non linear and hence cannot b written in the form of AX<=b. for some finite matrix A and vector b. describe a construction of an infinite number of linear constraints on x such that the feasible set for all of these constraints together is equal to the disk.
    Think about it geometrically. A point will lie inside the circle x^2+y^2=1 if it is on the same side of each tangent to the circle as the origin.

    The tangent to the circle at the point (\cos\theta,\sin\theta) has equation x\cos\theta+y\sin\theta=1. So the linear constraint will be x\cos\theta+y\sin\theta\leqslant1. If the point (x,y) satisfies that constraint for all \theta, then it will satisfy x^2+y^2\leqslant1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Linear Programming~Please help!
    Posted in the Math Topics Forum
    Replies: 5
    Last Post: April 13th 2010, 02:12 PM
  2. Replies: 1
    Last Post: November 17th 2008, 04:18 AM
  3. linear programming
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: May 25th 2008, 04:59 PM
  4. linear programming
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: May 25th 2008, 07:40 AM
  5. Linear Programming
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: February 19th 2008, 08:06 AM

Search Tags


/mathhelpforum @mathhelpforum