I am trying to solve the following minimization problem, perhaps by getting it into a LP form:
Let $u= [u_1, u_2, ...u_N]^T$ a column vector, and $v=[{1\over u_1}, {1 \over u_2}, ...{1 \over u_N}]^T$ a column vector of the reciprocals of elements in u. Let d be another column vector in $R^N$.
problem: find u that minimizes $d^Tv$ such that $1^Tu \le 1$ (i.e. $\sum u_i \le 1$)