Constrained optimization set up with at least one value constraint

Question

I am working through setting up a optimization problem as:

min Ax
s.t. x ≥ 0

Where A is of size 1xp and hence x has size px1.

How do I add a condition such that at least one of x has value 100.

Answer 1

You may write $$(x_1-100)(x_2-100)\cdots (x_p-100)=0$$if i get the question rightly. Also you may define $$y=x-100$$ and rewrite the optimization problem for sake of simplicity.