Abstract
Although there were some works on analog neural networks for sparse portfolio design, the existing works do not allow us to control the number of the selected assets and to adjust the weighting between the risk and return. This paper proposes a Lagrange programming neural network (LPNN) model for sparse portfolio design, in which we can control the number of selected assets. Since the objective function of the sparse portfolio design contains a non-differentiable \(\ell _1\)-norm term, we cannot directly use the LPNN approach. Hence, we propose a new formulation based on an approximation of the \(\ell _1\)-norm. In the theoretical side, we prove that state of the proposed LPNN network globally converges to the nearly optimal solution of the sparse portfolio design. The effectiveness of the proposed LPNN approach is verified by the numerical experiments. Simulation results show that the proposed analog approach is superior to the comparison analog neural network models.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Tank, D., Hopfield, J.: Simple’neural’optimization networks: An a/d converter, signal decision circuit, and a linear programming circuit. IEEE Trans. Circuits Syst. 33(5), 533–541 (1986)
Xia, Y., Leung, H., Wang, J.: A projection neural network and its application to constrained optimization problems. IEEE Trans. Circ Syst. I Fund. Theory Appl. 49(4), 447–458 (2002)
Bouzerdoum, A., Pattison, T.R.: Neural network for quadratic optimization with bound constraints. IEEE Trans. Neural Netw. 4(2), 293–304 (1993)
Wang, Y., Li, X., Wang, J.: A neurodynamic optimization approach to supervised feature selection via fractional programming. Neural Netw. 136, 194–206 (2021)
Feng, R., Leung, C.-S., Constantinides, A.G., Zeng, W.J.: Lagrange programming neural network for nondifferentiable optimization problems in sparse approximation. IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2395–2407 (2016)
Shi, Z., Wang, H., Leung, C.-S., So, H.C.: Robust MIMO radar target localization based on lagrange programming neural network. Signal Process. 174, 107574 (2020)
Liang, J., Leung, C.S., So, H.C.: Lagrange programming neural network approach for target localization in distributed MIMO radar. IEEE Trans. Signal Process. 64(6), 1574–1585 (2016)
Kremer, P.J., Lee, S., Bogdan, M., Paterlini, S.: Sparse portfolio selection via the sorted \(\ell _1\)-norm. J. Bank. Fin. 110, 105687 (2020)
Markowitz, H.: Portfolio selection. J. Fin. 7(1), 77–91 (1952)
Liu, Q., Guo, Z., Wang, J.: A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for dynamic portfolio optimization. Neural Netw. 26, 99–109 (2012)
Leung, M.F., Wang, J.: Minimax and biobjective portfolio selection based on collaborative neurodynamic optimization. IEEE Trans. Neural Netw. Learn. Syst. 32, 2825–2836 (2021)
Boyd, S., Parikh, N., Chu, N: Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers. Now Publishers Inc (2011)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Wang, H., Hui, D., Leung, CS. (2023). Lagrange Programming Neural Networks for Sparse Portfolio Design. In: Tanveer, M., Agarwal, S., Ozawa, S., Ekbal, A., Jatowt, A. (eds) Neural Information Processing. ICONIP 2022. Lecture Notes in Computer Science, vol 13624. Springer, Cham. https://doi.org/10.1007/978-3-031-30108-7_4
Download citation
DOI: https://doi.org/10.1007/978-3-031-30108-7_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-30107-0
Online ISBN: 978-3-031-30108-7
eBook Packages: Computer ScienceComputer Science (R0)