On the non-linear multilevel programming problems

In this paper a multilevel programming problem viz. three level programming problem (TPP) is considered. It involves three optimization problems where the constraint region of the first level problem is implicitly determined by two other optimization problems. The objective function of the first level is indefinite quadratic, the second one is linear and the third one is linear fractional. The feasible region is a convex polyhedron. At first it is shown that minimizing the indefinite quadratic programming problem is equivalent to minimizing a quasiconcave function over a feasible region composed of the faces of the convex polyhedron. Also, the second objective function being linear and the third being linear fractional, the optimal solution occurs at an extreme point. It is illustrated with the help of an example.