
Previous Article
The inverse parallel machine scheduling problem with minimum total completion time
 JIMO Home
 This Issue

Next Article
Substitution secant/finite difference method to large sparse minimax problems
LSSVM approximate solution for affine nonlinear systems with partially unknown functions
1.  Tianjin Key Laboratory of Process Measurement and Control, School of Electrical Engineering and Automation, Tianjin University, Tianjin, 300072, China, China, China 
2.  Department of Computing, Curtin University of Technology, Perth, WA 6102 
References:
[1] 
A. AkyyuzDascioglu and H. CerdikYaslan, The solution of highorder nonlinear ordinary differential equations by Chebyshev Series,, Applied Mathematics and Computation, 217 (2011), 5658. doi: 10.1016/j.amc.2010.12.044. Google Scholar 
[2] 
S. J. An, W. Q. Liu and S. Venkatesh, Fast Exact crossvalidation of least squares support vector machines,, Pattern Recognition, 40 (2007), 2154. Google Scholar 
[3] 
T. Falck, K. Pelckmans, J. A. K. Suykens and B. De Moor, Identification of WienerHammerstein Systems using LSSVMs,, 15th IFAC Symposium on System Identification, (2009). Google Scholar 
[4] 
Z. Guan and J. F. Lu, Basic of Numerical Analysis(Chinese),, 2nd edition, (2010). Google Scholar 
[5] 
A. Isidori, Nonlinear Control Systems: An Introduction,, 3rd edition, (1995). Google Scholar 
[6] 
D. R. Kincaid and E. W. Cheney, Numerical Analysis: Mathematics of Scientific Computing,, 3rd edition, (2002). Google Scholar 
[7] 
I. E. Lagaris, A. Likas and D. I. Fotiadis, Artificial neural networks for solving ordinary and partial differential equations,, IEEE Transactions on Neural Networks, 9 (1998), 987. doi: 10.1109/72.712178. Google Scholar 
[8] 
H. Lee and I. S. Kang, Neural algorithm for solving differential equations,, Journal of Computational Physics, 91 (1990), 110. doi: 10.1016/00219991(90)90007N. Google Scholar 
[9] 
K. S. McFall and J. R. Mahan, Artificial neural network method for solution of boundary value problems with exact satisfaction of arbitrary boundary conditions,, IEEE Transactions on Neural Networks, 20 (2009), 1221. doi: 10.1109/TNN.2009.2020735. Google Scholar 
[10] 
S. Mehrkanoon, T. Falck and J. A. K. Suykens, Approximate solutions to ordinary differential equations using least squares support vector machines,, IEEE Trans. on Neural Networks and Learning Systems, 23 (2012), 1356. doi: 10.1109/TNNLS.2012.2202126. Google Scholar 
[11] 
M. Popescu, On minimum quadratic functional control of affine nonlinear systems,, Nonlinear Analysis: Theory, 56 (2004), 1165. doi: 10.1016/j.na.2003.11.009. Google Scholar 
[12] 
J. I. Ramos, Linearization techniques for singular initialvalue problems of ordinary differential equations,, Applied Mathematics and Computation, 161 (2005), 525. doi: 10.1016/j.amc.2003.12.047. Google Scholar 
[13] 
P. Ramuhalli, L. Udpa and S. S. Udpa, Finiteelement neural networks for solving differential equations,, IEEE Transactions on Neural Networks, 16 (2005), 1381. doi: 10.1109/TNN.2005.857945. Google Scholar 
[14] 
J. A. K. Suykens, T. V. Gestel, J. Brabanter,B. D. Moor and J. Vandewalle, Least Squares Support Vector Machines,, 1st edition, (2002). Google Scholar 
[15] 
J. A. K. Suykens, J. Vandewalle and B. D. Moor, Optimal control by least squares support vector machines,, Neural Networks, 14 (2001), 23. doi: 10.1016/S08936080(00)000770. Google Scholar 
[16] 
I. G. Tsoulos, D. Gavrilis and E. Glavas, Solving differential equations with constructed neural networks,, Neurocomputing, 72 (2009), 2385. doi: 10.1016/j.neucom.2008.12.004. Google Scholar 
[17] 
V. Vapnik, The Nature of Statistical Learning Theory,, 1st edition, (). Google Scholar 
[18] 
A. M. Wazwaz, A new method for solving initial value problems in secondorder ordinary differential equations,, Applied Mathematics and Computation, 128 (2002), 45. doi: 10.1016/S00963003(01)000212. Google Scholar 
show all references
References:
[1] 
A. AkyyuzDascioglu and H. CerdikYaslan, The solution of highorder nonlinear ordinary differential equations by Chebyshev Series,, Applied Mathematics and Computation, 217 (2011), 5658. doi: 10.1016/j.amc.2010.12.044. Google Scholar 
[2] 
S. J. An, W. Q. Liu and S. Venkatesh, Fast Exact crossvalidation of least squares support vector machines,, Pattern Recognition, 40 (2007), 2154. Google Scholar 
[3] 
T. Falck, K. Pelckmans, J. A. K. Suykens and B. De Moor, Identification of WienerHammerstein Systems using LSSVMs,, 15th IFAC Symposium on System Identification, (2009). Google Scholar 
[4] 
Z. Guan and J. F. Lu, Basic of Numerical Analysis(Chinese),, 2nd edition, (2010). Google Scholar 
[5] 
A. Isidori, Nonlinear Control Systems: An Introduction,, 3rd edition, (1995). Google Scholar 
[6] 
D. R. Kincaid and E. W. Cheney, Numerical Analysis: Mathematics of Scientific Computing,, 3rd edition, (2002). Google Scholar 
[7] 
I. E. Lagaris, A. Likas and D. I. Fotiadis, Artificial neural networks for solving ordinary and partial differential equations,, IEEE Transactions on Neural Networks, 9 (1998), 987. doi: 10.1109/72.712178. Google Scholar 
[8] 
H. Lee and I. S. Kang, Neural algorithm for solving differential equations,, Journal of Computational Physics, 91 (1990), 110. doi: 10.1016/00219991(90)90007N. Google Scholar 
[9] 
K. S. McFall and J. R. Mahan, Artificial neural network method for solution of boundary value problems with exact satisfaction of arbitrary boundary conditions,, IEEE Transactions on Neural Networks, 20 (2009), 1221. doi: 10.1109/TNN.2009.2020735. Google Scholar 
[10] 
S. Mehrkanoon, T. Falck and J. A. K. Suykens, Approximate solutions to ordinary differential equations using least squares support vector machines,, IEEE Trans. on Neural Networks and Learning Systems, 23 (2012), 1356. doi: 10.1109/TNNLS.2012.2202126. Google Scholar 
[11] 
M. Popescu, On minimum quadratic functional control of affine nonlinear systems,, Nonlinear Analysis: Theory, 56 (2004), 1165. doi: 10.1016/j.na.2003.11.009. Google Scholar 
[12] 
J. I. Ramos, Linearization techniques for singular initialvalue problems of ordinary differential equations,, Applied Mathematics and Computation, 161 (2005), 525. doi: 10.1016/j.amc.2003.12.047. Google Scholar 
[13] 
P. Ramuhalli, L. Udpa and S. S. Udpa, Finiteelement neural networks for solving differential equations,, IEEE Transactions on Neural Networks, 16 (2005), 1381. doi: 10.1109/TNN.2005.857945. Google Scholar 
[14] 
J. A. K. Suykens, T. V. Gestel, J. Brabanter,B. D. Moor and J. Vandewalle, Least Squares Support Vector Machines,, 1st edition, (2002). Google Scholar 
[15] 
J. A. K. Suykens, J. Vandewalle and B. D. Moor, Optimal control by least squares support vector machines,, Neural Networks, 14 (2001), 23. doi: 10.1016/S08936080(00)000770. Google Scholar 
[16] 
I. G. Tsoulos, D. Gavrilis and E. Glavas, Solving differential equations with constructed neural networks,, Neurocomputing, 72 (2009), 2385. doi: 10.1016/j.neucom.2008.12.004. Google Scholar 
[17] 
V. Vapnik, The Nature of Statistical Learning Theory,, 1st edition, (). Google Scholar 
[18] 
A. M. Wazwaz, A new method for solving initial value problems in secondorder ordinary differential equations,, Applied Mathematics and Computation, 128 (2002), 45. doi: 10.1016/S00963003(01)000212. Google Scholar 
[1] 
Yanfei Lu, Qingfei Yin, Hongyi Li, Hongli Sun, Yunlei Yang, Muzhou Hou. Solving higher order nonlinear ordinary differential equations with least squares support vector machines. Journal of Industrial & Management Optimization, 2017, 13 (5) : 122. doi: 10.3934/jimo.2019012 
[2] 
Dengfeng Lü, Shuangjie Peng. On the positive vector solutions for nonlinear fractional Laplacian systems with linear coupling. Discrete & Continuous Dynamical Systems  A, 2017, 37 (6) : 33273352. doi: 10.3934/dcds.2017141 
[3] 
Uwe Schäfer, Marco Schnurr. A comparison of simple tests for accuracy of approximate solutions to nonlinear systems with uncertain data. Journal of Industrial & Management Optimization, 2006, 2 (4) : 425434. doi: 10.3934/jimo.2006.2.425 
[4] 
K. Schittkowski. Optimal parameter selection in support vector machines. Journal of Industrial & Management Optimization, 2005, 1 (4) : 465476. doi: 10.3934/jimo.2005.1.465 
[5] 
HongGunn Chew, ChengChew Lim. On regularisation parameter transformation of support vector machines. Journal of Industrial & Management Optimization, 2009, 5 (2) : 403415. doi: 10.3934/jimo.2009.5.403 
[6] 
Keiji Tatsumi, Masashi Akao, Ryo Kawachi, Tetsuzo Tanino. Performance evaluation of multiobjective multiclass support vector machines maximizing geometric margins. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 151169. doi: 10.3934/naco.2011.1.151 
[7] 
YaXiang Yuan. Recent advances in numerical methods for nonlinear equations and nonlinear least squares. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 1534. doi: 10.3934/naco.2011.1.15 
[8] 
Hassan Mohammad, Mohammed Yusuf Waziri, Sandra Augusta Santos. A brief survey of methods for solving nonlinear leastsquares problems. Numerical Algebra, Control & Optimization, 2019, 9 (1) : 113. doi: 10.3934/naco.2019001 
[9] 
Fengqiu Liu, Xiaoping Xue. Subgradientbased neural network for nonconvex optimization problems in support vector machines with indefinite kernels. Journal of Industrial & Management Optimization, 2016, 12 (1) : 285301. doi: 10.3934/jimo.2016.12.285 
[10] 
Ye Tian, Wei Yang, Gene Lai, Menghan Zhao. Predicting nonlife insurer's insolvency using nonkernel fuzzy quadratic surface support vector machines. Journal of Industrial & Management Optimization, 2019, 15 (2) : 985999. doi: 10.3934/jimo.2018081 
[11] 
Ying Gao, Xinmin Yang, Kok Lay Teo. Optimality conditions for approximate solutions of vector optimization problems. Journal of Industrial & Management Optimization, 2011, 7 (2) : 483496. doi: 10.3934/jimo.2011.7.483 
[12] 
Caiping Liu, Heungwing Lee. Lagrange multiplier rules for approximate solutions in vector optimization. Journal of Industrial & Management Optimization, 2012, 8 (3) : 749764. doi: 10.3934/jimo.2012.8.749 
[13] 
Jing Yang. Segregated vector Solutions for nonlinear Schrödinger systems with electromagnetic potentials. Communications on Pure & Applied Analysis, 2017, 16 (5) : 17851805. doi: 10.3934/cpaa.2017087 
[14] 
Yu Han, NanJing Huang. Some characterizations of the approximate solutions to generalized vector equilibrium problems. Journal of Industrial & Management Optimization, 2016, 12 (3) : 11351151. doi: 10.3934/jimo.2016.12.1135 
[15] 
Qi Wang, Yanren Hou. Determining an obstacle by farfield data measured at a few spots. Inverse Problems & Imaging, 2015, 9 (2) : 591600. doi: 10.3934/ipi.2015.9.591 
[16] 
Sigurdur F. Hafstein, Christopher M. Kellett, Huijuan Li. Computing continuous and piecewise affine lyapunov functions for nonlinear systems. Journal of Computational Dynamics, 2015, 2 (2) : 227246. doi: 10.3934/jcd.2015004 
[17] 
Fabio Punzo. Support properties of solutions to nonlinear parabolic equations with variable density in the hyperbolic space. Discrete & Continuous Dynamical Systems  S, 2012, 5 (3) : 657670. doi: 10.3934/dcdss.2012.5.657 
[18] 
Yohei Sato, ZhiQiang Wang. On the least energy signchanging solutions for a nonlinear elliptic system. Discrete & Continuous Dynamical Systems  A, 2015, 35 (5) : 21512164. doi: 10.3934/dcds.2015.35.2151 
[19] 
Mila Nikolova. Analytical bounds on the minimizers of (nonconvex) regularized leastsquares. Inverse Problems & Imaging, 2008, 2 (1) : 133149. doi: 10.3934/ipi.2008.2.133 
[20] 
Octavian G. Mustafa, Yuri V. Rogovchenko. Existence of square integrable solutions of perturbed nonlinear differential equations. Conference Publications, 2003, 2003 (Special) : 647655. doi: 10.3934/proc.2003.2003.647 
2018 Impact Factor: 1.025
Tools
Metrics
Other articles
by authors
[Back to Top]