The Optimistic Algorithm And Relative Properties On A Class Of Bi-level Nonlinear Programming Model

In this paper, discuss two kinds especial construction of nonlinear bi-level programming. One kind is LBPC (linear bi-level price control) model, other kind is QFBP(quadratic fractional bi-level programming)model that author proposed.In order to extend and refine relative properties and theory of LBPC, give two algorithms, that is Frank-Wolfe algorithm and Topkis-veinott revised algorithm. The main idea of Frank-Wolfe algorithm of LBPC, combines Kuhn-Tucker condition, exact penalty function and linearized method of Frank-Wolfe. So, this makes the problem simple. At the same time, some relative properties and theorems were obtained. But idea and method of Topkis-veinott revised algorithm of LBPC is simpler. The author uses Kuhn-Tucker condition and Topkis-veinott revised algorithm to transform the LBPC into a series of linear programming. After studying convergence, find this algorithm has better convergence. Finally, numerical computations respectively show that two algorithms are feasible and efficient.In order to extend and refine related results of nonlinear bi-level programming, give QFBP model, in which the leader's objective function is convex quadratic, but the follower's one is fractional, and Constraint condition is linear inequality. Then define model construction of QFBP and, what's more, do some especial studies in optimum condition. Based on Kuhn-Tucker condition and dual convex-quadratic programming, several optimality conditions, (that is weak duality theorem, strong duality theorem, a necessary and sufficient condition.) are derived. So these conditions extend and refine some known results in nonlinear programming; they also will be a power tool that applied in practice.