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
王琳 1洪陈春 2罗和治1
作者信息
- 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
- 折叠
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.
Abstract
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 a good 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/GUROBIKey words
sensitivity of parameters/portfolio selection/non-convex quadratically constrained quadratic programming/semi-definite programming relaxation/GUROBI引用本文复制引用
出版年
2024
NETL
NSTL
万方数据