A Primal Neural Network for Online Equality-Constrained Quadratic Programming
- 84 Downloads
This paper aims at solving online equality-constrained quadratic programming problem, which is widely encountered in science and engineering, e.g., computer vision and pattern recognition, digital signal processing, and robotics. Recurrent neural networks such as conventional GradientNet and ZhangNet are considered as powerful solvers for such a problem in light of its high computational efficiency and capability of circuit realisation. In this paper, an improved primal recurrent neural network and its electronic implementation are proposed and analysed. Compared to the existing recurrent networks, i.e. GradientNet and ZhangNet, our network can theoretically guarantee superior global exponential convergence. Robustness performance of our such neural model is also analysed under a large model implementation error, with the upper bound of stead-state solution error estimated. Simulation results demonstrate theoretical analysis on the proposed model, which also verify the effectiveness of the proposed model for online equality-constrained quadratic programming.
KeywordsRecurrent neural networks Online equality-constrained quadratic programming Global exponential convergence Robustness analysis
This work was supported in part by the National Natural Science Foundation of China under Grant 61773375, Grant 61375036, and Grant 61511130079, and in part by the Microsoft Collaborative Research Project, and by the Academy of Finland under No.298700.
Compliance with Ethical Standards
Conflict of interests
The authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
- 1.Chen K, Jia K, Zhang Z, Kämäräinen JK. Spectral attribute learning for visual regression. Pattern Recogn. 2017; (66):74–81. in press.Google Scholar
- 2.Chen K, Loy CC, Gong S, Xiang T. Feature mining for localised crowd counting. British Machine Vision Conference; 2012. p. 21.1–21.11.Google Scholar
- 3.Chen K, Gong S, Xiang T, Loy CC. Cumulative attribute space for age and crowd density estimation. IEEE Conference on Computer Vision and Pattern Recognition; 2013. p. 2467–2474.Google Scholar
- 6.Chen K, Zhang L, Zhang Y. Cyclic motion generation of multi-link planar robot performing square end-effector trajectory analyzed via gradient-descent and Zhang et al’s neural-dynamic methods. International Symposium on Systems and Control in Aerospace and Astronautics; 2008. p. 1–6.Google Scholar
- 7.Wang J, Zhang Y. Recurrent neural networks for real-time computation of inverse kinematics of redundant manipulators. Machine Intelligence: Quo Vadis. 2004;299–319.Google Scholar
- 12.Suykens J, Van Gestel T, De Brabanter J, De Moor B, Vandewalle J, Suykens J, Van Gestel T. 2002. Least squares support vector machines. vol 4 World Scientific.Google Scholar
- 15.Zhang Y, Leithead WE, Leith DJ. Time-series Gaussian process regression based on Toeplitz computation of O(N 2) operations and O(N)-level storage. IEEE Conference on Decision and Control; 2005. p. 3711–3716.Google Scholar
- 18.Zhang Y. Towards piecewise-linear primal neural networks for optimization and redundant robotics. IEEE International Conference on Networking, Sensing and Control; 2006. p. 374–379.Google Scholar
- 21.Chen K. Recurrent implicit dynamics for online matrix inversion. Appl Math Comput 2013;219(20):10218–24.Google Scholar
- 22.Chen K, Yi C. Robustness analysis of a hybrid of recursive neural dynamics for online matrix inversion. Appl Math Comput 2016;273:969–75.Google Scholar
- 27.Zhang Y, Li S, Zhang X. Simulink comparison of varying-parameter convergent-differential neural-network and gradient neural network for solving online linear time-varying equations. World Congress on Intelligent Control and Automation; 2016. p. 887–894.Google Scholar
- 28.Zhang Z, Chen S, Zheng L, Zhang J. Matlab Simulink of varying-parameter convergent-differential neural-network for solving online time-varying matrix inverse. International Symposium on Computational Intelligence and Design; 2016. p. 320–325.Google Scholar
- 29.Chen K, Guo D, Tan Z, Yang Z, Zhang Y. Cyclic motion planning of redundant robot arms: simple extension of performance index may not work. International Symposium on Intelligent Information Technology Application; 2008. p. 635– 639.Google Scholar
- 30.Mead C, Ismail M. 1989. Analog VLSI implementation of neural systems. Springer Science & Business Media.Google Scholar
- 35.Chen K, Zhang Z. An Improved Recurrent Network for Online Equality-Constrained Quadratic Programming. Advances in Brain Inspired Cognitive Systems; 2016. p. 1–10.Google Scholar