Minimization of a quasi-convex function over a efficient set

The nonconvex programming problem of minimizing a quasi-concave function over an efficient (or weakly efficient) set of a multiobjective linear program is studied. A cutting plane algorithm which finds an approximate optimal solution in a finite number of steps is developed. For the particular ‘all linear’ case the algorithm performs better, finding an optimal solution in a finite time, and being more easily implemented.