不等式约束优化问题的改进光滑l_(1)精确罚函数法  

Improved Smooth l_(1) Exact Penalty Function Method for Inequality Constrained Optimization Problems

作　　者：徐奥 房明磊 盛雨婷 丁德凤 XU Ao;FANG Ming-lei;SHENG Yu-ting;DING De-feng(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽准南232001

出　　处：《数学的实践与认识》2025年第2期158-168,共11页Mathematics in Practice and Theory

基　　金：中国煤炭教育协会高等教育分会教改立项研究课题(2021MXJG175);安徽省高等学校省级质量工程项目(2022xsxx050);安徽省高校自然科学研究重点项目(KJ2021A0451)。

摘　　要：针对不等式约束优化问题的l_(1)精确罚函数,利用光滑技术,构建了一个改进的二次连续可微的惩罚函数和光滑惩罚问题,基于光滑惩罚问题,提出了一种解决不等式约束优化问题的算法.在适当的条件下,证明了光滑惩罚问题的最优解是原问题的近似最优解,进一步验证了算法的收敛性,并通过几个数值算例来说明算法的性能,初步数值结果表明该算法的可行性和有效性。Aiming at the l_(1) exact penalty function of inequality constrained optimization problem,an improved quadratic continuous differentiable penalty function and a smooth penalty problem are constructed by using the smooth technique.Under appropriate conditions,it is proved that the optimal solution of the smooth penalty problem is the approximate optimal solution of the original problem,and the convergence of the algorithm is further verified.Several numerical examples are given to illustrate the performance of the algorithm,and the preliminary numerical results show the feasibility and effectiveness of the algorithm.

关 键 词：不等式约束优化 l_(1)精确罚函数 光滑技术 近似最优解 

分 类 号：G63[文化科学—教育学]