A new approach to the problem of minimizing a quartic (fourth order) cost function, subject to linear constraints, is presented. A « satisficing range » is introduced for each variable (i.e. a range in which all values of the variable are considered to entail the same minimal cost), leading to a new linear formulation (« range programming »). Improvements in results over previous approaches are reported for a specific example (due to Goodman), and should be expected in general.
LAURENT, G. (1976). Range Programming: Introducing a « Satisficing Range » in a L.P. Management Science, 22(6), pp. 713-716.