Research On The Equilibrium Point Algorithms For Nonlinear Bilevel Programs

This paper discusses the two types of special nonlinear bilevel programming problems and their algorithms. It is mainly composed of three parts.In the first part, we introduce Manoel Campelo's algorithms for the linear bilevel programming with only non-negative in the upper level, which find the equilibrium point for this linear bilevel programming by means of the simplex method.In the second part, we consider the nonlinearly bilevel programming and give its algorithm by means of Maneol's algorithm for the equilibrium point. Finally, we present some numerical examples to demonstrate the concrete steps of the algorithm.In the third part, inspired by Maneol's work for the linear bilevel programming, we consider the bilevel programming which is obtained by replacing the upper ob-jective function in the original Maneol's model with a quadratic concave function, and give its algorithm by means of the simplex method for linear programming and Lemke algorithm for the quadratic programming with linear constraints, and show its local optimality. Finally, we present some numerical examples to demonstrate the concrete steps of the algorithm.