Abstract
The Lagrange programming neural network (LPNN) is a framework for solving constrained nonlinear programm problems. But it can solve differentiable objective/contraint functions only. As the \(l_1\)-norm constrained quadratic minimization (L1CQM), one of the sparse approximation problems, contains the nondifferentiable constraint, the LPNN cannot be used for solving L1CQM. This paper formulates a new LPNN model, based on introducing hidden states, for solving the L1CQM problem. Besides, we discuss the stability properties of the new LPNN model. Simulation shows that the performance of the LPNN is similar to that of the conventional numerical method.
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Acknowledgement
The work was supported by a research grant from City University of Hong Kong (Project No.: 7004233).
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Lee, C.M., Feng, R., Leung, CS. (2015). Lagrange Programming Neural Network for the \(l_1\)-norm Constrained Quadratic Minimization. In: Arik, S., Huang, T., Lai, W., Liu, Q. (eds) Neural Information Processing. ICONIP 2015. Lecture Notes in Computer Science(), vol 9491. Springer, Cham. https://doi.org/10.1007/978-3-319-26555-1_14
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DOI: https://doi.org/10.1007/978-3-319-26555-1_14
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