带参数敏感度的最优权衡投资组合问题的半定规划松弛  

Semi-definite programming relaxation for optimal trade-off portfolio selection with sensitivity of parameters

作　　者：王琳 洪陈春[2] 罗和治 WANG Lin;HONG Chenchun;LUO Hezhi(School of Science,Zhejiang Sci-Tech University,Hangzhou 310018,China;Huaxin Consulting Co.,Ltd.,Hangzhou 310014,China)

机构地区：[1]浙江理工大学理学院,杭州310018 [2]华信咨询设计研究院有限公司,杭州310014

出　　处：《浙江理工大学学报（自然科学版）》2024年第6期861-866,共6页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：国家自然科学基金项目(12271485,11871433);浙江省自然科学基金项目(LZ21A010003)。

摘　　要：考虑带参数敏感度的最优权衡投资组合问题,其模型是一个非凸非可微优化问题,其中目标函数含有极大和极小函数。将该优化问题变换为一个等价的非凸二次约束二次规划问题,提出了等价变换问题的一个紧的半定规划松弛,并估计了其与原问题之间的间隙。数值结果表明,该半定规划松弛可以有效找到大多数测试问题的全局最优解,且计算时间优于求解器GUROBI,从而为寻求问题的一个好的近似解提供方法。In this paper,we consider the optimal trade-off portfolio problem with parameter sensitivity.For this problem,the model is a non-convex and non-differentiable optimization problem in which the objective function contains the maximum and minimum functions.This optimization problem is transformed into an equivalent non-convex quadratically constrained quadratic programming problem.A tight semi-definite programming relaxation for the equivalent transformation problem is proposed and the gap between it and the original problem is estimated.The numerical results show that the semi-definite programming relaxation can effectively find the global optimal solution of most test problems,and the computational time is less than that of the solver GUROBI.It can provide a method for finding agood approximate solution to the problem.

关 键 词：参数敏感度 投资组合 非凸二次约束二次规划 半定规划松弛 GUROBI 

分 类 号：O224[理学—运筹学与控制论]