Algorithms for nonlinear bilevel mathematical programs

The bilevel programming problem (BLPP) is a model of a leader-follower game in which play is sequential and cooperation is not permitted. Some basic properties of the general model are developed, and a conjecture relevant to solution procedures is presented. Two algorithms are presented for solving various versions of the game when certain convexity conditions hold. One algorithm relies upon a hybrid branch-and-bound scheme and does not guarantee global optimality. Another is based on objective function cuts and, barring numerical stability problems with the optimizer, is guaranteed to converge to an ε-optimal solution. The performance of the two algorithms is examined using randomly generated test problems. The computational performance of the branch-and-bound algorithm is explored, and the cutting-plane algorithm is used to determine whether or not the branch-and-bound algorithm is uncovering global optima