1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

D-admissible directions and extermal points

  1. Feb 5, 2008 #1
    Let X = C[a,b], J(y) = integ(a to b) sin^3(x) + y(x)^2 dx and D={yEX; integ(a to b) y(x)dx = 1}
    (a) what are the D-admissible directions for J?
    (b) Find all possible (local) external points for J on D?

    so far i have:
    (let e be epsilon)
    lim e->0 J(y+ev) - J(y) / e
    = lim e->0 integ (a to b) [ sin^3(x) + (y+ev)^2(x)dx - J(y) ] / e
    = lim e->0 integ (a to b) [2ey(x)v(x) + e^2v(x)^2) dx ] / e
    = 2 integ(a to b) y(x)v(x) dx
    A similar example was done in class, so i just copied it for this question.
    G(y) = integ(a to b) y(x) dx = 1
    gateaux G(y;v) = integ (a to b) y(x)v(x) dx

    is this right so far? how do i go about answering (a) and (b).
  2. jcsd
  3. Feb 6, 2008 #2
    i was wondering if the D-admissible directions for J is just
    y+Ev E D
    integ (a-b) (y+Ev)(x) dx
    = 1+ E integ(a-b) v(x) dx

    can i simplify any further?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook