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

作　　者：杜梦琪 徐梦薇 段庆松 DU Meng-qi;XU Meng-wei;DUAN Qing-song(College of Science,Hebei University of Technology,Tianjin 300401,China;Intelligent Risk Control Center,BOC Financial Technology Company Limited,Shanghai 200120,China)

机构地区：[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

出　　处：《高校应用数学学报（A辑）》2024年第2期182-198,共17页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11901556,12071342);河北省自然科学基金(A2020202030)。

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.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 

分 类 号：O224[理学—运筹学与控制论]