Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: A point of a closed convex set?

  1. Jun 25, 2007 #1
    1. The problem statement, all variables and given/known data

    Given D a a closed convex in R4 which consists of points [tex](1,x_2,x_3,x_4)[/tex] which satisfies that that [tex]0\leq x_2,0 \leq x_3 [/tex] and that [tex] x_2^2 - x_3 \leq 0[/tex]

    3. The attempt at a solution

    Then to show that either the point a: = (1,-1,0,1) or b:=(1,0,0,-1) is part of the convex set D.

    They must satisfy the equation [tex]l = b \cdot t + (1-t) \cdot b [/tex] and

    [tex]l = a \cdot t + (1-t) \cdot a [/tex] which proves that either of the two points lies on a line segment l which belongs to the convex set.

    Am I on the right track?
  2. jcsd
  3. Jun 26, 2007 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You want to show that a and b belong to D?

    D has be entirely defined, and the fact that it is convex doesn't have anything to do with the problem as far as i can see. The second coordinate of a is negative, so it violates [tex]0\leq x_2[/tex].
  4. Jun 26, 2007 #3


    User Avatar
    Science Advisor

    And b is almost as trivial!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook