A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for dynamic portfolio optimization

• Published in: Neural networks Vol. 26; pp. 99 - 109
• Main Authors: Liu, Qingshan, Guo, Zhishan, Wang, Jun
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-02-2012; Elsevier
• Subjects: Algorithms; Animals; Applied sciences; Artificial intelligence; Computer science; control theory; systems; Computer Simulation; Connectionism. Neural networks; Convergence; Differential inclusion; Exact sciences and technology; Flows in networks. Combinatorial problems; Humans; Lyapunov function; Mathematical programming; Neural Networks (Computer); Nonlinear Dynamics; Operational research and scientific management; Operational research. Management science; Pattern Recognition, Automated; Portfolio theory; Pseudoconvex optimization; Recurrent neural networks; Recurrent neural networks; Differential inclusion; Pseudoconvex optimization; Convergence; Lyapunov function; Lower bound; Recurrent neural nets; Network management; Neural network; Modeling; Constrained optimization; Efficiency; Equality constraint; Dynamic programming; Fractional programming; Rational function; Portfolio management; Optimal flow; Mathematical programming
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2011.09.001

In this paper, a one-layer recurrent neural network is proposed for solving pseudoconvex optimization problems subject to linear equality and bound constraints. Compared with the existing neural networks for optimization (e.g., the projection neural networks), the proposed neural network is capable of solving more general pseudoconvex optimization problems with equality and bound constraints. Moreover, it is capable of solving constrained fractional programming problems as a special case. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed as long as the designed parameters in the model are larger than the derived lower bounds. Numerical examples with simulation results illustrate the effectiveness and characteristics of the proposed neural network. In addition, an application for dynamic portfolio optimization is discussed.