Nonlinear goal programming with −ni, −pi and −(ni+pi) goals

The (minimizing) achievement function of the traditional Goal Programming (GP) model has five basic forms: n_i, p_i, (n_i+p_i), (n_i-p_i), and (p_i-n_i), where n_i and p_i are th nonnegative under and over achievement variables in the i goal-constraint. Zhang and Shang (2001) proposed the theory of Goal Programs with -n_i, -p_i, and -(n_i+p_i) goals, which has many interesting and practical applications. This paper extends the theory further into the nonlinear situation and proposes a new algorithm for solving the ensuing nonconvex nonlinear program. Results obtained in this paper shows that the basic conclusions for the linear GP model still hold for the nonlinear case.