最优去杠杆化问题的新分枝定界算法  

A new branch-and-bound algorithm for optimal deleveraging problem

作　　者：罗和治[1] 张宏伟 

机构地区：[1]浙江工业大学经贸管理学院,浙江杭州310023 [2]浙江工业大学理学院,浙江杭州310023

出　　处：《浙江工业大学学报》2018年第2期233-236,共4页Journal of Zhejiang University of Technology

基　　金：国家自然科学基金资助项目(11371324);浙江省自然科学基金资助项目(LY17A010023)

摘　　要：在不限制临时性和永久性价格影响的大小关系下,最优去杠杆化问题可归结为一个带有箱子和二次约束的非凸二次规划问题,它是NP难问题.现有的拉格朗日方法未能保证找到问题的全局最优解.结合二次凸松弛技术和拉格朗日方法,提出了求最优去杠杆化问题全局最优解的新分枝定界算法,其中下界由拉格朗日方法得到,而上界由二次凸松弛求得,分析了算法的全局收敛性.数值结果表明:该算法可以有效地找到最优去杠杆化问题的全局最优解.With no restrictions on the relative magnitudes of permanent and temporary price impact,the optimal deleveraging problem reduces to a nonconvex quadratic program with quadratic and box constraints,which is NP-hard.The existing Lagrange method can not guarantee to find the global optimal solution of the optimal deleveraging problem.In this paper,by combining the quadratic convex relaxation technique and the Lagrange method,we propose a new branch-and-bound algorithm to find the global optimal solution of the optimal deleveraging problem,where the lower bound is obtained by the Lagrange method and the upper bound is computed by the quadratic convex relaxation.Then we analyze the global convergence of the proposed algorithm.Computational results indicate that the algorithm can effectively find the global optimal solution of the optimal deleveraging problem.

关 键 词：最优去杠杆 临时性和永久性价格影响 非凸二次规划 凸松弛 分枝定界算法 

分 类 号：O221.2[理学—运筹学与控制论]