非线性约束两分块非凸优化问题一个新的分裂序列二次规划算法  

A New Splitting Sequential Quadratic Programming Algorithm for Two-block Nonconvex Optimization Problems with Nonlinear Constraints

作　　者：马国栋 何天广 罗煜 MA Guodong;HE Tianguang;LUO Yu(School of Mathematics Sciences,Center for Applied Mathematics of Guangxi,Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis,Guangxi Minzu University,Nanning 530006,China)

机构地区：[1]广西民族大学数学科学学院,广西应用数学中心,广西混杂计算与集成电路设计分析重点实验室,广西南宁530006

出　　处：《广西民族大学学报(自然科学版)》2024年第4期66-72,共7页Journal of Guangxi Minzu University :Natural Science Edition

基　　金：国家自然科学基金项目(12261008);广西自然科学基金项目(2023GXNSFAA026158);广西大学生创新创业训练计划项目(S202310608005)。

摘　　要：研究了非线性约束两分块非凸优化问题的降维方法,基于交替方向乘子法(AD-MM)和序列二次规划(SQP)算法思想,提出了一个新型分裂SQP算法。首先,以SQP算法为主线,原问题的二次规划(QP)子问题的增广拉格朗日问题植入AD-MM思想,通过求解两个小规模QP子问题产生算法的搜索方向。其次,以增广拉格朗日函数作为效益函数,沿搜索方向进行Armijo线搜索得到算法步长。在较弱的假设下,分析了算法的全局收敛性。In this paper,the splitting and dimensionality reduction method for two-block nonconvex optimization problems with nonlinear constraints is studied,based on the alternating direction multiplier method(ADMM)and sequential quadratic programming(SQP)algorithm,a new splitting SQP algorithm is proposed.Firstly,taking SQP algorithm as the main line,the augmented Lagrange problem of quadratic programming(QP)subproblem for the original problem is implanted with ADMM idea,and the search direction of the algorithm is generated by solving two small-scale QP subproblems.Secondly,the augmented Lagrangian function is used as the merit function,and the step length is obtained by Armijo line search along the search direction.Finally,under the suitable assumptions,the global convergence of the new algorithm is analyzed.

关 键 词：两分块非凸优化 非线性等式约束 分裂SQP算法 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]