Disjoint双线性规划的一个混合整数线性规划变换及其应用

A mixed integer linear programming reformulation for disjoint bilinear programming and its applications

针对disjoint双线性规划问题,给出了一个混合整数线性规划变换方法,以求得其全局最优解。该方法将disjoint双线性规划变换为一个带有互补约束的线性规划,并利用0-1变量和大M法线性化互补约束。同时,将该方法应用于金融系统中的不确定性系统性风险估计问题,证明了该问题可变换为一个disjoint双线性规划问题,进而利用所提出的方法求解。数值结果表明:提出的方法能有效找到中大规模最坏情形系统性风险估计问题的全局最优解,并优于已有的全局解方法。

In this paper,a mixed integer linear programming reformulation approach for finding the global optimal solution to disjoint bilinear programming was proposed.Through the reformulation of disjoint bilinear programming into as a linear program with complementarity constraints,the complementarity constraints were linearized by using binary variables and big-M methods.Moreover,through the application of this method to estimate the uncertain systemic risk in financial systems,it was proved that this problem can be transformed into a disjoint bilinear programming problem,which could be solved by the proposed method.The numerical results indicate that the proposed method significantly outperforms the existing global solution approach by finding a global optimal solution to medium-and large-scale worst-case systemic risk estimation problem.