二阶微分方程方法求解带不等式约束的优化问题  

Second-Order Differential Equation Method for Solving Optimization Problems with Inequality Constraints

作　　者：李思怡 姜莹 宁文琪 任泓燃 

机构地区：[1]沈阳航空航天大学理学院,辽宁 沈阳

出　　处：《理论数学》2024年第12期1-6,共6页Pure Mathematics

摘　　要：针对只含有不等式约束的优化问题,本文首先给出了其Karush-Kuhn-Tucker (KKT)条件,并利用光滑互补函数将KKT系统转化为一类光滑的方程组问题;其次,将光滑方程组问题转化为无约束优化问题;最后,本文提出一类二阶微分方程系统求解无约束优化问题,并讨论了二阶微分方程系统的解的稳定性及收敛速度。For optimization problems with only inequality constraints, this paper first presents their Karush-Kuhn-Tucker (KKT) conditions, and uses smooth complementarity functions to transform the KKT system into a class of smooth system of equations problems. Secondly, this article transforms the problem of smooth equation systems into an unconstrained optimization problem. Finally, this article proposes a class of second-order differential equation systems for solving unconstrained optimization problems, and discusses the stability and convergence speed of the solutions of second-order differential equation systems.

关 键 词：二阶微分方程系统 不等式约束优化问题 KKT条件 

分 类 号：O17[理学—数学]