ARTIFICIAL VARIABLE

Artificial variable - A variable, say v, added to an equation, h(x) = 0. The resulting system, h(x) + v = 0, is feasible upon letting v = -h(x) for a chosen x. Then, the objective function is modified to penalize nonzero values of v. Often, v >= 0 is required, multiplying h by -1, if necessary, to get started. This grew from linear programming , where a Phase I objective is used to find a solution with v=0 (or ascertain that the original system has no feasible solution ) by minimizing Sum_i(v_i) (ignoring the original objective, cx).