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.