Abstract
A neural network algorithm for second-order conic programming is proposed. By the Smooth technique, a smooth and convex energy function is constructed. We have proved that for any initial point, every trajectory of the neural network converges to an optimal solution of the second-order conic programming. The simulation results show the proposed neural network is feasible and efficient.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Lobo, M.S., Vandenberghe, L., Boyd, S., Lebret, H.: Application of Second Order Cone Programming. Linear Algebra and its Applications 284, 193–228 (1998)
Lebret, H., Boyd, S.: Antenna Array Pattern Synthesis via Convex Optimization. IEEE Transactions on Signal Processing 45, 526–532 (1997)
Lu, W.S., Hinamoto, T.: Optimal Design of IIR Digital Filters with Robust Stability Using Conic-Quadratic-Programming Updates. IEEE Transactions on Signal Processing 51, 1581–1592 (2003)
Wang, J.: A Deterministic Annealing Neural Network for Conex Programming. Neural networks 7, 629–641 (1994)
Jiang, D., Wang, J.: A Recurrent Neural Network for Real-time Semidefinite Programming. IEEE Transaction on Neural Networks 10, 81–93 (1999)
Leung, Y., Chen, K., Jiao, Y., Gao, X., Leung, K.S.: A New Gradient-Based Neural Network for Solving Linear and Quadratic Programming Problems. IEEE Transactions on Neural Networks 12, 1074–1083 (2001)
Benson, H.Y., Vanderbei, R.J.: Solving Problems with Semidefinite and Related Constraints Using Interior-Point Methods for Nonlinear Programming. Math. Program 95, 279–302 (2003)
Avriel, M.: Nonlinear Programming: Analysis and Methods. Prentice-Hall, Englewood Cliffs (1976)
Scalle, J.L., Lefschetz, S.: Stability by Lyapunov’s Direct Method with Applications. Academic, New York (1961)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mu, X., Liu, S., Zhang, Y. (2005). A Neural Network Algorithm for Second-Order Conic Programming. In: Wang, J., Liao, X., Yi, Z. (eds) Advances in Neural Networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, vol 3496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11427391_115
Download citation
DOI: https://doi.org/10.1007/11427391_115
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25912-1
Online ISBN: 978-3-540-32065-4
eBook Packages: Computer ScienceComputer Science (R0)