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In this paper a multilevel programming problem, that is, three level programming problem 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. Considering the relationship between feasible solutions to the problem and bases of the coefficient sub-matrix associated to the variables of the third level, an enumerative algorithm is proposed, which finds an optimum solution to the given problem. It is illustrated with the help of an example.

An enumerative algorithm for non-linear multi-level integer programming problem