Abstract
In view of its fundamental role arising in numerous fields of science and engineering, the problem of online solving quadratic programs (QP) has been investigated extensively for the past decades. One of the state-of-the-art recurrent neural network (RNN) solvers is dual neural network (DNN). The dual neural network is of simple piecewise-linear dynamics and has global convergence to optimal solutions. Its exponential-convergence property relies on a so-called exponential convergence condition. Such a condition often exists in practice but seems difficult to be proved. In this paper, we investigate the proof complexity of such a condition by analyzing its one-dimensional case. The analysis shows that in general the exponential convergence condition often exists for dual neural networks, and always exists at least for the one-dimensional case. In addition, the analysis is very complex.
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References
Zhang, Y., Wang, J.: A Dual Neural Network for Convex Quadratic Programming Subject to Linear Equality and Inequality Constraints. Physics Letters A, 298, 271–278 (2002)
Zhang, Y., Wang, J., Xu, Y.: A Dual Neural Network for Bi-Criteria Kinematic Control of Redundant Manipulators. IEEE Transactions on Robotics and Automation 18, 923–931 (2002)
Zhang, Y., Ge, S.S., Lee, T.H.: A Unified Quadratic Programming Based Dynamical System Approach to Joint Torque Optimization of Physically Constrained Redundant Manipulators. IEEE Transactions on Systems, Man, and Cybernetics 34, 2126–2133 (2004)
Zhang, Y.: On the LVI-Based Primal-Dual Neural Network for Solving Online Linear and Quadratic Programming Problems. Proceedings of American Control Conference 1351–1356 (2005)
Zhang, Y.: Minimum-Energy Redundancy Resolution Unified by Quadratic Programming. In: The 15th International Symposium on Measurement and Control in Robotics, Belgium (2005)
Zhang, Y.: Towards Piecewise-Linear Primal Neural Networks for Optimization and Redundant Robotics. In: Proceedings of IEEE International Conference on Networking, Sensing and Control, pp. 374–379. IEEE Computer Society Press, Los Alamitos (2006)
Zhang, Y.: Inverse-Free Computation for Infinity-Norm Torque Minimization of Robot Manipulators. Mechatronics 16, 177–184 (2006)
Zhang, Y.: A Set of Nonlinear Equations and Inequalities Arising in Robotics and its Online Solution via a Primal Neural Network. Neurocomputing 70, 513–524 (2006)
Latash, M.L.: Control of Human Movement. Human Kinetics Publisher, Chicago (1993)
Zhang, X., Chaffin, D.B.: An Inter-Segment Allocation Strategy for Postural Control in Human Reach Motions Revealed by Differential Inverse Kinematics and Optimization. In: Proceedings of IEEE International Conference on Systems, Man, and Cybernetics, pp. 469–474. IEEE Computer Society Press, Los Alamitos (1997)
Iqbal, K., Pai, Y.C.: Predicted Region of Stability for Balance Recovery: Motion at the Knee Joint can Improve Termination of Forward Movement. Journal of Biomechanics 33, 1619–1627 (2000)
Zhang, Y., Wang, J.: Global Exponential Stability of Recurrent Neural Networks for Synthesizing Linear Feedback Control Systems via Pole Assignment. IEEE Transactions on Neural Networks, 13, 633–644 (2002)
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Zhang, Y., Peng, H. (2007). One-Dimensional Analysis of Exponential Convergence Condition for Dual Neural Network. In: Huang, DS., Heutte, L., Loog, M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2007. Lecture Notes in Computer Science(), vol 4682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74205-0_16
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DOI: https://doi.org/10.1007/978-3-540-74205-0_16
Publisher Name: Springer, Berlin, Heidelberg
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