Results 1 to 2 of 2

Math Help - linear programming proofs

  1. #1
    Member
    Joined
    Apr 2008
    From
    Seoul, South Korea
    Posts
    128

    linear programming proofs

    i have these two questions that i am having trouble understanding.

    1. show that the linear kuhn-tucker theorem implies the complementary slackness conditions.

    2. show that if A is a linear transformation and A' is the dual transformation, then the matrices of A and A' in the standard bases are transposes of each other.

    i'm not sure if i'm understanding what the linear kuhn-tucker theorem is saying, because i have found many versions of it, but none of them were comprehensible for me.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Apr 2008
    From
    Seoul, South Korea
    Posts
    128
    just as information, the linear kuhn tucker thm states that x* in R^m is a solution to the linear programming problem <c_f|x>=f(x) ->min and Ax<=b if and only if there exists a vector y* in R^n, y*>=0 such that L(x*,y)<=L(x*,y*)<=L(x,y*) for all x in R^m and all y in R^n with y>=0

    the complementary slackness condition says that such (x*,y*) satisfying this condition also satisfies y_k*(g_k(x*)-b_k)=0 for 1<=k<=n

    *note L(x,y) is the lagrange function L(x,y)=<c_f|x>+<Ax-b|y>
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help me with linear programming
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 13th 2011, 04:52 PM
  2. Linear Alegebra linear equations proofs
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 13th 2010, 10:47 AM
  3. Replies: 1
    Last Post: November 17th 2008, 04:18 AM
  4. Linear Programming
    Posted in the Advanced Applied Math Forum
    Replies: 6
    Last Post: July 15th 2008, 04:57 AM
  5. help linear programming
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: February 7th 2007, 01:30 AM

Search Tags


/mathhelpforum @mathhelpforum