求解双层规划问题的松弛序列二次规划方法
A relaxed sequence quadratic programming method for solving bilevel programming problems
杜梦琪 1徐梦薇 1段庆松2
作者信息
- 1. 河北工业大学理学院,天津 300401
- 2. 中银金融科技有限公司智能风控中心,上海 200120
- 折叠
摘要
考虑一类具有特殊结构的双层规划问题,其下层问题为凸问题.首先通过内点罚方法将下层的约束函数惩罚到目标函数,使得下层问题近似为一系列无约束优化问题.然后使用KKT条件替换无约束的下层问题的最优解集,那么双层规划问题被一系列松弛的单层问题近似.文中设计了一种光滑的序列二次规划算法求解该松弛问题,并证明了当罚因子趋近于0时,该算法生成的迭代点列收敛到双层规划问题的弱稳定点.数值实验验证了算法的可行性.
Abstract
This article considers a class of bilevel programming problems with a special structure,where the lower-level problems are convex problems.First,the constraint function of the lower-level problem is penalized to the objective function by the interior point penalty method,so that the lower-level problem is approximated as a series of unconstrained optimiza-tion problems.Then the optimal set of solutions of the unconstrained lower-level problems is replaced by the KKT condition,and then the bilevel programming problem is approximated by a series of relaxed single-level problems.This article designs a smooth sequential quadratic programming algorithm to solve the relaxation problem and show that the iteration sequence generated by the algorithm converges to the weakly stationary point of the bilevel program-ming problem when the penalty factor converges to zero.The numerical experiments verify the feasibility of the algorithm.
关键词
双层规划/Tikhonov-regularized/interior-penalty/序列二次规划方法Key words
bilevel program/Tikhonov-regularized interior-penalty/sequential quadratic programming algorithm引用本文复制引用
基金项目
国家自然科学基金(11901556)
国家自然科学基金(12071342)
河北省自然科学基金(A2020202030)
出版年
2024
NETL
NSTL
万方数据