English

运筹学学报 >

2023 , Vol. 27 >Issue 1: 103 - 114

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2023.01.007

 

基于递归型神经网络动力学求解时变凸二次规划

展开
  • 1. 中原工学院电子信息学院, 河南郑州 451191
周军, E-mail: jz970077409@sina.com

收稿日期: 2020-10-22

  网络出版日期: 2023-03-16

基金资助

国家自然科学基金(61876209);国家自然科学基金(62076222)

收起

Recurrent neural network dynamic for time-varying convex quadratic programming

Expand
  • 1. School of Electronic and Information, Zhongyuan University of Technology, Zhengzhou 451191, Henan, China

Received date: 2020-10-22

  Online published: 2023-03-16

Fold

摘要

为了在线求解时变凸二次规划问题，实现误差精度更高、求解时间更短和收敛速度更快的目标。本文采用了求解问题更快的时变网络设计参数，选择了有限时间可以收敛的Sign-bi-power激活函数，构造了一种改进的归零神经网络动力学模型。其后，分析了模型的稳定性和收敛性，得到其解能够在有限时间内收敛。最后，在仿真算例中，与传统的梯度神经网络和归零神经网络模型相比，所提模型具有更高的误差精度、更短的求解时间和更快的收敛速度，优于前两种网络模型。

关键词： 时变凸二次规划; 改进的归零动力学模型; Sign-bi-power

本文引用格式

廖伍代, 周军 . 基于递归型神经网络动力学求解时变凸二次规划[J]. 运筹学学报, 2023 , 27(1) : 103 -114 . DOI: 10.15960/j.cnki.issn.1007-6093.2023.01.007

Abstract

When solving a time-varying convex quadratic programming problem online, in order to achieve the requirements of higher error accuracy, shorter solution time and faster convergence speed, this paper designs and constructs an improved zeroing neurodynamic model of the design parameters of the time-varying network. Firstly, the Lyapunov stability theory proves that the network model is globally progressively stable. Subsequently, it is proved that when it uses the Sign-bi-power activation function, it is guaranteed that its solution can converge for a finite time. Finally, in the simulation example, compared with the gradient neural network model and the zeroing neural network model, the zeroing neurodynamics of the time-varying network design parameters is better than the two network models in solving the time-convex quadratic programming problem, with higher error accuracy, shorter solution time and faster convergence speed.

Key words： time-varying convex quadratic programming; improved zeroing dynamic model; Sign-bi-power

参考文献

1 王建建, 何枫, 吴子轩, 等. 改进区间可接受度的证券投资组合区间二次规划模型[J]. 中国管理科学, 2018, 26 (9): 11- 18.
2 唐程辉, 张凡, 张宁, 等. 基于风电场总功率条件分布的电力系统经济调度二次规划方法[J]. 电工技术学报, 2019, 34 (10): 2069- 2078.
3 刘耘臻, 万志强, 杨超. 飞行载荷外部气动力的二次规划等效映射方法[J]. 北京航空航天大学学报, 2020, 46 (3): 541- 547.
4 王冠宇, 丁亮, 高海波, 等. 增强爬坡能力的六足机器人分步二次规划足力分配算法及试验验证[J]. 机械工程学报, 2019, 55 (21): 11- 20.
5 Li X , Zhang M . Interior-point algorithm for linear optimization based on a new trigonometric kernel function[J]. Operations Research Letters, 2015, 43 (5): 471- 475.
6 冯江华, 王斌, 胡云卿, 等. 地铁列车运行过程的线性二次型最优建模及内点算法求解[J]. 控制与信息技术, 2018, (1): 1- 6.
7 张思颖. 凸二次规划SDP松弛解的存在性证明[J]. 重庆工商大学学报(自然科学版), 2020, 37 (3): 66- 69.
8 刘颖, 赵迪. 求解凸二次规划的主对偶积极集法[J]. 哈尔滨师范大学(自然科学版), 2011, 27 (2): 40- 43.
9 赵营峰, 刘三阳, 葛立. 求解不定二次约束二次规划问题的全局优化算法[J]. 工程数学学报, 2018, 35 (4): 367- 374.
10 Wang J . Recurrent neural networks for solving linear matrix equations[J]. Computers and Mathematics with Applications, 1993, 26 (9): 23- 34.
11 Wang J . A recurrent neural network for real-time matrix inversion[J]. Applied Mathematics and Computation, 1993, 55, 89- 100.
12 Zhang Y , Jiang D , Wang J . A recurrent neural network for solving Sylvester equation with time-varying coefficients[J]. IEEE Trans Neural Netw, 2002, 13 (5): 1053- 1063.
13 Zhang Y , Wang J . Recurrent neural networks for nonlinear output regulation[J]. Automatica, 2001, 37 (8): 1161- 1173.
14 Zhang Y , Chen K , Tan H Z . Performance analysis of gradient neural network exploited for online time-varying matrix inversion[J]. IEEE Transactions on Automatic Control, 2009, 54, 1940- 1945.
15 Guo D , Zhang Y . Zhang neural network, Getz-Marsden dynamic system, and discrete-time algorithms for time-varying matrix inversion with application to robots' kinematic control[J]. Neurocomputing, 2012, 97, 22- 32.
16 Xiao L , Tan H , Jia L , et al. New error function designs for finite-time ZNN models with application to dynamic matrix inversion[J]. Neurocomputing, 2020, 402, 395- 408.
17 Zhang Y , Ge S S . Design and analysis of a general recurrent neural network model for time-varying matrix inversion[J]. IEEE Transactions on Neural Networks, 2005, 16 (6): 1477- 1490.
18 Zhang Y , Yi C , Ma W . Simulation and verification of Zhang neural network for online time-varying matrix inversion[J]. Simulation Modelling Practice and Theory, 2009, 17 (10): 1603- 1617.
19 Li S , Chen S , Liu B . Accelerating a recurrent neural network to finite-time convergence for solving time-varying sylvester equation by using a Sign-bi-power activation function[J]. Neural Processing Letters, 2013, 37 (2): 189- 205.
20 Xiao L , Liao B . A convergence-accelerated Zhang neural network and its solution application to Lyapunov equation[J]. Neurocomputing, 2016, 193, 213- 218.
21 Xiao L , Liao B , Shuai L , et al. Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations[J]. Neural Networks, 2018, 98, 102- 113.
22 Lv X , Xiao L , Tan Z . Improved Zhang neural network with finite-time convergence for time-varying linear system of equations solving[J]. Information Processing Letters, 2019, 147, 88- 93.
23 Wang X , Liang L , Che M . Finite-time convergent complex-valued neural networks for the time-varying complex linear matrix equations[J]. Engineering Letters, 2018, 26 (4): 432- 440.
24 Zhang Z , Zheng L , Wang M . An exponential-enhanced-type varying parameter RNN for solving time-varying matrix inversion[J]. Neurocomputing, 2019, 338, 126- 138.
25 Zhang Y , Li Z . Zhang neural network for online solution of time-varying convex quadratic program subject to time-varying linear-equality constraints[J]. Physics Letters A, 2009, 373, 18- 19.
26 Qin S , Feng J , Song J , et al. A one-layer recurrent neural network for constrained complex-variable convex optimization[J]. IEEE Transactions on Neural Networks & Learning Systems, 2018, 29 (3): 534- 544.
27 Jin L , Li S . Nonconvex function activated zeroing neural network models for dynamic quadratic programming subject to equality and inequality constraints[J]. Neurocomputing, 2017, 267, 107- 113.
28 Jiang D , Wang J . A recurrent neural network for real-time semidefinite programming[J]. Applied Mathematics and Computation, 1993, 55 (1): 89- 100.
29 Ma Q , Qin S , Jin T . Complex Zhang neural networks for complex-variable dynamic quadratic programming[J]. Neurocomputing, 2019, 330, 56- 69.
30 Huang X , Lou X , Cui B . A novel neural network for solving convex quadratic programming problems subject to equality and inequality constraints[J]. Neurocomputing, 2016, 214, 23- 31.
31 Effati S , Ranjbar M . A novel recurrent nonlinear neural network for solving quadratic programming problems[J]. Applied Mathematical Modelling, 2011, 35 (4): 1688- 1695.
32 杨静俐, 吴艺团, 陈锦奎. 求解凸二次规划的连续型神经网络模型[J]. 梧州学院学报, 2018, 28 (3): 15- 21.
33 肖林, 严慧玲, 周文辉. 求解二次规划问题的快速收敛梯度神经网络模型设计及仿真[J]. 湖南文理学院学报(自然科学版), 2016, 28 (1): 51- 54+59.
34 Wa ng , J . Recurrent neural network for solving quadratic programming problems with equality constraints[J]. Electronics Letters, 1992, 28 (14): 1345- 1347.
35 袁亚湘, 孙文瑜. 最优化理论与方法[M]. 北京: 科学出版社, 2007.
36 郭田德, 韩丛英. 从数值最优化方法到学习最优化方法[J]. 运筹学学报, 2019, 23 (4): 1- 12.
37 戎卫东, 马毅. 集值映射向量优化问题的$ \varepsilon$-真有效解(英文)[J]. 运筹学学报, 2000, 4 (4): 21- 32.
38 杨新民, 赵克全. 向量优化问题的近似解研究[J]. 运筹学学报, 2017, 21 (4): 1- 18.
39 戴彧虹, 刘新为. 线性与非线性规划算法与理论[J]. 运筹学学报, 2014, 18 (1): 69- 92.
40 李浙宁, 凌晨, 王宜举, 等. 张量分析和多项式优化的若干进展[J]. 运筹学学报, 2014, 18 (1): 134- 148.
Options
文章导航

/

〈 〉