A new approach to non-linear programming is presented. The original non-linear programming problem is formulated as a sequence of unconstrained optimization problems. It is shown that this sequence will converge to the non-linear programming optimum. The proposed negative-positive harrier function has certain advantages over the usual barrier and penalty function methods. In addition, by minor modification of the new unconstrained objective function it is possible from a single optimization to see if there exists a feasible region.