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The QL mathematical programming formulation is

(2.37a)

subject to

(2.37b)

(2.37c)

(2.37d)

(2.37e)

If the general formulation (2.36) is to be recast as a mathematical programming problem, it is necessary to include (i) a binary variable vector b, (ii) a positive variable vector s, and (iii) two sets of constraints (2.37b). The resulting formulation (2.37) is a mixed integer nonlinear problem.

Again, the set of constraints (2.37e) of problem (2.37) can be relaxed, leading to a nonlinear problem, whose optimal solution generally meets constraints (2.37e).