解多项式双层规划最优解的参数化方法

Parametric global optimization for polynomial bilevel programming

给出解多项式双层规划最优解的参数化算法.以上层变量为参数,对双层规划下层利用参数化方法求解;得到合理反应集代入上层,使双层问题转化为多项式规划求解.证明了算法的收敛性,数值例子表明算法是可行的.

A parametric global optimization algorithm is proposed for solving polynomial bilevel programming problem in this paper. We first describe how we can recast and solve the follower＇s problem of the bileve fomulation as a multi-parametric programming problem, with parameters being the variables of the leader＇s problem. By inserting the obtained reasonable response sets in the leader＇ problem the overall problem is transformed into a set of independent polynomial programming problem. Convergence of the algorithm is established and numerical results are given to show the feasibility.