广西师范大学学报（自然科学版） ›› 2024, Vol. 42 ›› Issue (5): 101-109.doi: 10.16088/j.issn.1001-6600.2023110802

• 研究论文 • 上一篇    下一篇

一种基于罚函数法解决非光滑伪凸优化问题的神经网络算法及其应用

黄镘潼, 喻昕*   

  1. 广西大学 计算机与电子信息学院,广西 南宁 530004
  • 收稿日期:2023-11-08 修回日期:2024-02-20 出版日期:2024-09-25 发布日期:2024-10-11
  • 通讯作者: 喻昕(1973—),男,重庆人,广西大学教授,博士,博导。E-mail: yuxin21@126.com
  • 基金资助:
    国家自然科学基金(61862004)

A Neural Network Algorithm Based on Penalty Function Method for Solving Non-smooth Pseudoconvex Optimization Problems and Its Applications

HUANG Mantong, YU Xin*   

  1. School of Computer, Electronics and Information, Guangxi University, Nanning Guangxi 530004, China
  • Received:2023-11-08 Revised:2024-02-20 Online:2024-09-25 Published:2024-10-11

PDF (PC)

42

摘要： 针对实际应用中遇到的非光滑伪凸优化问题,本文提出一种创新的解决方案——结合罚函数理念和微分包含理论的单层神经网络算法。首先,通过数学理论证明,本文算法能够使状态解最终收敛至伪凸优化问题的最优解,从而确立所提出算法的正确性;其次,通过对2个数值实验的模拟收敛结果进行分析,进一步验证算法的有效性;最后,用本文算法解决实际应用问题,展示其在解决伪凸优化问题上的实际应用价值。与现有的神经网络算法相比,本文算法不仅能够解决更一般的具有凸不等式和等式约束的伪凸优化问题,也可以解决实际应用问题。此外,本文算法层次结构简单,无需计算精确的罚参数,可以选取任意初始点,无需添加任何辅助变量,为伪凸优化问题的解决提供一种有效途径。

关键词: 神经网络, 伪凸优化, 最优解, 罚函数, 实际应用

Abstract: To address the nonsmooth pseudoconvex optimization problems encountered in practical applications,an innovative solution is proposed:a single-layer neural network algorithm that integrates the concept of penalty functions and the theory of differential inclusions. Firstly,through mathematical theory,it is proved that this algorithm can ensure that the state solutions ultimately converge to the optimal solution of the pseudoconvex optimization problem,thus establishing the correctness of the proposed algorithm. Secondly,the effectiveness of the algorithm is further verified through the analysis of simulated convergence results from two numerical experiments. Finally,the applications of this algorithm to practical problems demonstrate its practical application value in solving pseudoconvex optimization issues. Compared with existing neural network algorithms,this algorithm can not only solve more general pseudoconvex optimization problems with convex inequality and equality constraints but also tackle practical application issues. Moreover,the algorithm has a simple hierarchical structure,does not require the calculation of precise penalty parameters,allows for the selection of any starting point,and does not add any auxiliary variable, which thus provides an effective approach to solving pseudoconvex optimization problems.

Key words: neural network, pseudoconvex optimization, optimal solution, penalty function, practical application

中图分类号:  TP183

[1] HOPFIELD J J,TANK D W. “Neural” computation of decisions in optimization problems[J]. Biological Cybernetics,1985,52 (3):141-152. DOI: 10.1007/BF00339943.
[2] XUE X P,BIAN W. Subgradient-based neural networks for nonsmooth convex optimization problems[J]. IEEE Transactions on Circuits and Systems I:Regular Papers,2008,55(8):2378-2391. DOI: 10.1109/TCSI.2008.920131.
[3] BIAN W,XUE X P. Subgradient-based neural networks for nonsmooth nonconvex optimization problems[J]. IEEE Transactions on Neural Networks,2009,20(6):1024-1038. DOI: 10.1109/TNN.2009.2016340.
[4] GAO X B,LIAO L Z. A new projection-based neural network for constrained variational inequalities[J].IEEE Transactions on Neural Networks,2009,20(3):373-388. DOI: 10.1109/TNN.2008.2006263.
[5] YANG J,HE X,HUANG T W. Neurodynamic approaches for sparse recovery problem with linear inequality constraints[J]. Neural Networks,2022,155:592-601. DOI: 10.1016/j.neunet.2022.09.013.
[6] BIAN W,CHEN X J. Neural network for nonsmooth,nonconvex constrained minimization via smooth approximation[J]. IEEE Transactions on Neural Networks and Learning Systems,2014,25(3):545-556. DOI: 10.1109/TNNLS.2013.2278427.
[7] QIN S T,XUE X P. A two-layer recurrent neural network for nonsmooth convex optimization problems[J]. IEEE Transactions on Neural Networks and Learning Systems,2015,26(6):1149-1160. DOI: 10.1109/TNNLS.2014.2334364.
[8] ZHAO Y,LIAO X F,HE X,et al. Centralized and collective neurodynamic optimization approaches for sparse signal reconstruction via L1-minimization[J]. IEEE Transactions on Neural Networks and Learning Systems,2022,33(12):7488-7501. DOI: 10.1109/TNNLS.2021.3085314.
[9] LI W J,BIAN W,XUE X P. Projected neural network for a class of non-Lipschitz optimization problems with linear constraints[J]. IEEE Transactions on Neural Networks and Learning Systems,2020,31(9):3361-3373. DOI: 10.1109/TNNLS.2019.2944388.
[10] YU X,WU L Z,XU C H,et al. A novel neural network for solving nonsmooth nonconvex optimization problems[J]. IEEE Transactions on Neural Networks and Learning Systems,2020,31(5):1475-1488. DOI: 10.1109/TNNLS.2019.2920408.
[11] LIU Q S,GUO Z S,WANG J. A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for dynamic portfolio optimization[J]. Neural Networks,2012,26:99-109. DOI: 10.1016/j.neunet.2011.09.001.
[12] QIN S T,YANG X D,XUE X P,et al. A one-layer recurrent neural network for pseudoconvex optimization problems with equality and inequality constraints[J]. IEEE Transactions on Cybernetics,2017,47(10):3063-3074. DOI: 10.1109/TCYB.2016.2567449.
[13] LIU N,QIN S T. A neurodynamic approach to nonlinear optimization problems with affine equality and convex inequality constraints[J]. Neural Networks,2019,109:147-158. DOI: 10.1016/j.neunet.2018.10.010.
[14] LI Q F,LIU Y Q,ZHU L K. Neural network for nonsmooth pseudoconvex optimization with general constraints[J]. Neurocomputing,2014,131:336-347. DOI: 10.1016/j.neucom.2013.10.008.
[15] LIU J X,LIAO X F. A projection neural network to nonsmooth constrained pseudoconvex optimization[J]. IEEE Transactions on Neural Networks and Learning Systems,2023,34(4):2001-2015. DOI: 10.1109/TNNLS.2021.3105732.
[16] XU C,CHAI Y Y,QIN S T,et al. A neurodynamic approach to nonsmooth constrained pseudoconvex optimization problem[J]. Neural Networks,2020,124:180-192. DOI: 10.1016/j.neunet.2019.12.015.
[17] LIU N,WANG J,QIN S T. A one-layer recurrent neural network for nonsmooth pseudoconvex optimization with quasiconvex inequality and affine equality constraints[J]. Neural Networks,2022,147:1-9. DOI: 10.1016/j.neunet.2021.12.001.
[18] PENOT J P,QUANG P H. Generalized convexity of functions and generalized monotonicity of set-valued maps[J]. Journal of Optimization Theory and Applications,1997,92(2):343-356. DOI: 10.1023/A:1022659230603.
[19] 喻昕,陈昭蓉. 一类非光滑非凸优化问题的神经网络方法[J]. 计算机应用研究,2019,36(9):2575-2578. DOI: 10.19734/j.issn.1001-3695.2018.03.0150.
[20] AUBIN J P,CELLINA A. Differential inclusions[M]. Berlin:Springer-Verlag,1984.
[21] SHI X L,WEN G H,YU X H. A discontinuous projection-based algorithm for solving distributed optimization with linear equation constraints[C] // 2020 39th Chinese Control Conference(CCC). Piscataway, NJ: IEEE, 2020:4884-4888. DOI: 10.23919/CCC50068.2020.9189464.
[22] CHENG L,HUO Z G,LIN Y Z,et al. Recurrent neural network for non-smooth convex optimization problems with application to the identification of genetic regulatory networks[J]. IEEE Transactions on Neural Networks,2011,22(5):714-726. DOI: 10.1109/TNN.2011.2109735.
[23] 耿焕同,周征礼,沈俊烨,等. 面向约束超多目标优化的双阶段搜索策略研究[J]. 计算机工程与应用,2023,59(7):80-91. DOI: 10.3778/j.issn.1002-8331.2207-0167.
[24] 胡竣涛,时小虎,马德印. 基于均值漂移和遗传算法的护工调度算法[J]. 广西师范大学学报(自然科学版),2021,39(3):27-39. DOI: 10.16088/j.issn.1001-6600.2020061703.
[25] 梁晓萍,罗晓曙. 基于遗传自适应的维纳滤波图像去模糊算法[J]. 广西师范大学学报(自然科学版),2017,35(4):17-23. DOI: 10.16088/j.issn.1001-6600.2017.04.003.
[26] 朱兴淋,汪廷华,赖志勇. 混合策略改进的金豺优化算法[J]. 计算机工程与应用,2024,60(4):99-112. DOI: 10.3778/j.issn.1002-8331.2306-0099.
[27] 符强,孔健明,纪元法,等.基于改进粒子群优化PDI的双补偿时钟同步算法[J].桂林电子科技大学学报,2023,43(1):27-34. DOI: 10.16725/j.cnki.cn45-1351/tn.2023.01.011.
[28] 张潇,宋威. 径向基函数神经网络指导的粒子群优化算法求解多峰优化问题[J]. 小型微型计算机系统,2023,44(11):2529-2537. DOI: 10.20009/j.cnki.21-1106/TP.2022-0163.
[29] 陈森朋,吴佳,陈修云. 基于强化学习的超参数优化方法[J]. 小型微型计算机系统,2020,41(4):679-684. DOI: 10.3969/j.issn.1000-1220.2020.04.002.
[30] 马勇健,史旭华,王佩瑶. 基于两阶段搜索与动态资源分配的约束多目标进化算法[J]. 计算机应用,2024,44(1):269-277. DOI: 10.11772/j.issn.1001-9081.2023010012.
[31] 王波,王浩,杜晓昕,等. 基于亚群和差分进化的混合蜻蜓算法[J]. 计算机应用,2023,43(9):2868-2876. DOI: 10.11772/j.issn.1001-9081.2022060813.
[1] 王天雨, 袁嘉伟, 齐芮, 李洋. 多类型知识增强的微博立场检测模型[J]. 广西师范大学学报（自然科学版）, 2024, 42(1): 79-90.
[2] 高飞, 郭晓斌, 袁冬芳, 曹富军. 改进PINNs方法求解边界层对流占优扩散方程[J]. 广西师范大学学报（自然科学版）, 2023, 41(6): 33-50.
[3] 周桥, 翟江涛, 荚东升, 孙浩翔. 基于卷积门控循环神经网络的Web攻击检测方法[J]. 广西师范大学学报（自然科学版）, 2023, 41(6): 51-61.
[4] 吴正清, 曹晖, 刘宝锴. 基于注意力卷积神经网络的中文虚假评论检测[J]. 广西师范大学学报（自然科学版）, 2023, 41(5): 26-36.
[5] 欧阳舒歆, 王洺钧, 荣垂田, 孙华波. 基于改进LSTM的多维QAR数据异常检测[J]. 广西师范大学学报（自然科学版）, 2023, 41(5): 49-60.
[6] 唐侯清, 辛斌斌, 朱虹谕, 乙加伟, 张冬冬, 武新章, 双丰. 基于多尺度注意力倒残差网络的轴承故障诊断[J]. 广西师范大学学报（自然科学版）, 2023, 41(4): 109-122.
[7] 韩欣月, 邓长征, 付添, 夏鹏雨, 刘旋. 基于MWOA-Elman神经网络的接地网瞬变电磁缺陷识别[J]. 广西师范大学学报（自然科学版）, 2023, 41(3): 53-66.
[8] 杨烁祯, 张珑, 王建华, 张恒远. 声音事件检测综述[J]. 广西师范大学学报（自然科学版）, 2023, 41(2): 1-18.
[9] 潘海明, 陈庆锋, 邱杰, 何乃旭, 刘春雨, 杜晓敬. 基于卷积推理的多跳知识图谱问答算法[J]. 广西师范大学学报（自然科学版）, 2023, 41(1): 102-112.
[10] 张涛, 杜建民. 基于无人机遥感的荒漠草原微斑块识别研究[J]. 广西师范大学学报（自然科学版）, 2022, 40(6): 50-58.
[11] 肖飞, 康增彦, 王维红. 两种算法用于预测A2/O工艺脱氮条件[J]. 广西师范大学学报（自然科学版）, 2022, 40(6): 173-184.
[12] 郝雅茹, 董力, 许可, 李先贤. 预训练语言模型的可解释性研究进展[J]. 广西师范大学学报（自然科学版）, 2022, 40(5): 59-71.
[13] 田晟, 宋霖. 基于CNN和Bagging集成的交通标志识别[J]. 广西师范大学学报（自然科学版）, 2022, 40(4): 35-46.
[14] 周圣凯, 富丽贞, 宋文爱. 基于深度学习的短文本语义相似度计算模型[J]. 广西师范大学学报（自然科学版）, 2022, 40(3): 49-56.
[15] 彭涛, 唐经, 何凯, 胡新荣, 刘军平, 何儒汉. 基于多步态特征融合的情感识别[J]. 广西师范大学学报（自然科学版）, 2022, 40(3): 104-111.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 李文博, 董青, 刘超, 张奇. 基于对比学习的儿科问诊对话细粒度意图识别[J]. 广西师范大学学报（自然科学版）, 2024, 42(4): 1 -10 .
[2] 高盛祥, 杨元樟, 王琳钦, 莫尚斌, 余正涛, 董凌. 面向域外说话人适应场景的多层级解耦个性化语音合成[J]. 广西师范大学学报（自然科学版）, 2024, 42(4): 11 -21 .
[3] 朱格格, 黄安书, 覃盈盈. 基于Web of Science的国际红树林研究发展态势分析[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 1 -12 .
[4] 何静, 冯元柳, 邵靖雯. 基于CiteSpace的多源数据融合研究进展[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 13 -27 .
[5] 左钧元, 李欣彤, 曾子涵, 梁超, 蔡进军. 金属有机骨架基催化剂在糠醛选择性加氢反应中的应用研究进展[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 28 -38 .
[6] 谭全伟, 薛贵军, 谢文举. 基于VMD和RDC-Informer的短期供热负荷预测模型[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 39 -51 .
[7] 刘畅平, 宋树祥, 蒋品群, 岑明灿. 基于开关电容的差分无源N通道滤波器[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 52 -60 .
[8] 王党树, 孙龙, 董振, 贾如琳, 杨黎康, 吴家驹, 王新霞. 变化负载下全桥LLC谐振变换器参数优化设计[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 61 -71 .
[9] 张锦忠, 韦笃取. PMSM混沌系统无初始状态约束的固定时间有界控制[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 72 -78 .
[10] 涂智荣, 凌海英, 李帼, 陆声链, 钱婷婷, 陈明. 基于改进YOLOv7-Tiny的轻量化百香果检测方法[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 79 -90 .
版权所有 © 广西师范大学学报（自然科学版）编辑部
地址：广西桂林市三里店育才路15号　邮编：541004
电话：0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发