AN ITERATIVE ALGORITHM FOR A CLASS OF NONLINEAR INTEGER BILEVEL PROGRAMMING PROBLEMS WITH BOX CONSTRAINTS

Abstract

The bilevel programming problem is a leader–follower game in which two players try to maximize their own objective functions over a common constraint region. This paper discusses an integer nonlinear bilevel programming problem with box constraints by exploiting the quasimonotone character of the indefinite quadratic fractional function, considered as leader's objective. By making use of the duality theory, given nonlinear bilevel programming problem is transformed into single level programming problem. Various cuts have been discussed in this paper which successively rank and scan all integer feasible points of the single level programming problem in the decreasing value of objective function. An iterative algorithm is proposed, which by making use of these cuts repeatedly, solves the problem.