Hierarchical optimization method for a class of nonlinear bilevel programming problems

A novel method for a class of nonlinear bilevel programming problems is proposed. By introducing a (decoupling) vector, a bilevel programming problem is decomposed into independent optimization sub-problems, which are easily solved at level 1 of a two-level hierarchical structure. At level 2 the decoupling vector is then updated (using) solutions from level 1. Based on decomposition-coordination principle, the proposed method can finally solve the optimal solution of the bilevel programming problem in an iterative fashion. For programming problems with (integers,) continualization technique is employed and continualized problems can be easily solved using the proposed method. Numerical examples are used to demonstrate simplicity and effectiveness of the proposed method.