Abstract
A new recurrent neural network is presented to solve a general quadratic programming problem in real time. In contrast with the available neural networks, the new neural network is with fewer neurons for solving quadratic programming problems. The global convergence of the model is proven with contraction analysis. The discrete time model and an alternative model for solving the problem under irredundant equality constraints are also studied. Simulation results demonstrate that the proposed recurrent neural networks are effective.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Hughes, T., Mierle, K.: Recurrent neural networks for voice activity detection. In: IEEE International Conference on Acoustics, pp. 7378–7382 (2013)
Schuster, M., Paliwal, K.K.: Bidirectional recurrent neural networks. IEEE Trans. Signal Process. 45(11), 2673–2681 (2002)
Scardino, L., Niess, R.: Performance of recurrent neural networks applied to a simplified pattern recognition problem. J. Comput. Sci. Colleges 15(3), 251–258 (2000)
Nan, B., Fukuda, O.: EMG-based motion discrimination using a novel recurrent neural network. J. Intell. Inf. Syst. 21(2), 113–126 (2003)
Zhang, Y.N., Tan, Z.G.: Repetitive motion of redundant robots planned by three kinds of recurrent neural networks and illustrated with a four-link planar manipulator’s straight-line example. Robot. Auton. Syst. 57(6–7), 645–651 (2009)
Vázquez, L.A., Jurado, F.: Decentralized identification and control in real-time of a robot manipulator via recurrent wavelet first-order neural network. In: Mathematical models in Engineering, pp. 1–12 (2015)
Xu, R., Wunsch, D.: Inference of genetic regulatory networks with recurrent neural network models using particle swarm optimization. IEEE Trans. Comput. Biol. 4(4), 681–692 (2007)
Hopfield, J.J.: Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Nat. Acad. Sci. 81(10), 3088–3092 (1984)
Liu, Q., Wang, J.: A one-layer recurrent neural network with a discontinuous hard-limiting activation function for quadratic programming. IEEE Trans. Neural Netw. 19(4), 558–570 (2008)
Mestari, M., Namir, A.: Switched capacitor neural networks for optimal control of nonlinear dynamic systems: design and stability analysis. Syst. Anal. Model. Simul. 41(3), 11–20 (2001)
Malek, A., Alipour, M.: Numerical solution for linear and quadratic programming problems using a recurrent neural network. Appl. Math. Comput. 192(1), 27–39 (2007)
Liu, Q., Wang, J.: A one-layer recurrent neural network with a discontinuous activation function for linear programming. Neural Comput. 20(5), 1366–1383 (2008)
Hu, X., Wang, J.: An improved dual neural network for solving a class of quadratic programming problems and its k-winners-take-all application. IEEE Trans. Neural Netw. 19(12), 2022–2031 (2008)
Xia, Y., Han, Y.W.: A mixed-binary convex quadratic reformulation for box-constrained nonconvex quadratic integer program. Mathematics 10(12), 7897–7905 (2014)
Li, S., Chen, S.: Decentralized kinematic control of a class of collaborative redundant manipulators via recurrent neural networks. Neurocomputing 91(9), 1–10 (2012)
Cheng, L., Hou, Z.: A Simplified Neural Network for Linear Matrix Inequality Problems. Neural Process. Lett. 29(3), 213–230 (2009)
Hu, X., Zhang, B.: A simplified dual neural network for quadratic programming with its KWTA application. IEEE Trans. Neural Netw. 17(6), 1500–1510 (2006)
Xia, Y., Feng, G., Wang, J.: A novel recurrent neural network for solving nonlinear optimization problems with inequality constraints. IEEE Trans. Neural Netw. 19, 1340–1353 (2008)
Tymoshchuk, P.: A discrete-time dynamic K-winners-take-all neural circuit. Neurocomputing 72(13–15), 3191–3202 (2009)
Xiao, Y., Liu, Y.: Analysis on the convergence time of dual neural network-based KWTA. IEEE Trans. Neural Netw. Learn. Syst. 23(4), 676–682 (2012)
Hu, F., Zhang, Z.: Contraction theory-based adaptive dynamic surface control for a class of nonlinear systems. Control Decis. 31(5), 769–775 (2016)
Wang, W., Slotine, J.J.E.: Contraction analysis of time-delayed communications and group cooperation. IEEE Trans. Autom. Control 51(4), 712–717 (2006)
Acknowledgements
The authors would like to acknowledge the support of Guangdong Science Foundation of China under Grant No. S2011010006116 and No. 2015A030313587, Shenzhen Science Technology Project No. JCYJ20150417094158025, No. JCY20160307100530069 and GRCK20170424095924228,Shenzhen Institute of Information Technology Scientific Research Platform Cultivation Project (PT201704).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Chen, S., Han, X., Tang, F., Lin, G. (2018). A New Recurrent Neural Network with Fewer Neurons for Quadratic Programming Problems. In: Li, K., Li, W., Chen, Z., Liu, Y. (eds) Computational Intelligence and Intelligent Systems. ISICA 2017. Communications in Computer and Information Science, vol 873. Springer, Singapore. https://doi.org/10.1007/978-981-13-1648-7_1
Download citation
DOI: https://doi.org/10.1007/978-981-13-1648-7_1
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-1647-0
Online ISBN: 978-981-13-1648-7
eBook Packages: Computer ScienceComputer Science (R0)