Converting Nonlinear Program into an LP

I have a problem with a nonlinear objective function which is

\begin{align}\min&\quad Z_j\cdot(N_j)^{0.5}\end{align} where $$j$$ is the index.

I want to know how can I turn it into a linear programming problem.

• Welcome to OR.SE! Can you provide more information? What are $Z_j$ and $N_j$? Are they binary and continuous? Are they both continuous? Also, you can format your question better by using MathJax
– EhsanK
Jan 26 '20 at 4:01
• In addition to questions by @EhsanK, what constraints if any are there? Jan 26 '20 at 12:17
• Also, are $Z,N$ both optimization variables? Are they matrices? Jan 26 '20 at 17:56
• Z is a binary variable and Nj is the summation of Xij on i which X is also a binary variable( which makes the N an integer). This is actually an uncapacitated facility location problem and the part I wrote is the setup cost. Feb 1 '20 at 21:42