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Homework Help: Linear Programming proof

  1. Oct 7, 2013 #1
    1. The problem statement, all variables and given/known data

    Let c in R^n be a parameter and consider the following function of c:

    f(c)= minimize cx
    subject to Ax=b
    x>/= 0

    where x is an n-dimensional decision vector, A is an mxn matrix, and b is an m-dimensional constant. The function f(c) is determined by solving the above linear program for a particular value of the parameter c. Show that f(c) is concave.

    3. The attempt at a solution

    Let x^1 be solution to the linear program when c=c^1 and x^2 be the solution when c=c^2

    I need to show the following: f(Lc^1 +(1-L)c^2) >/= Lf(c^1) + (1-L)f(c^2)

    the RHS is Lx^1+(1-L)x^2, but I'm not sure what to do with the LHS. It means solving an LP with an objective function of Lc^1x + (1-L)c^2x
  2. jcsd
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