A Novel Neurodynamic Approach to Constrained Complex-Variable Pseudoconvex Optimization

• Published in: IEEE transactions on cybernetics Vol. 49; no. 11; pp. 3946 - 3956
• Main Authors: Liu, Na, Qin, Sitian
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.11.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Beamforming; Complex-variable pseudoconvex optimization; Complexity; Constraints; Convergence; Linear programming; Lyapunov function; Neural networks; Neurodynamics; Optimization; Penalty function; Programming; recurrent neural network; Recurrent neural networks; time-varying penalty
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2018.2855724

Complex-variable pseudoconvex optimization has been widely used in numerous scientific and engineering optimization problems. A neurodynamic approach is proposed in this paper for complex-variable pseudoconvex optimization problems subject to bound and linear equality constraints. An efficient penalty function is introduced to guarantee the boundedness of the state of the presented neural network, and make the state enter the feasible region of the considered optimization in finite time and stay there thereafter. The state is also shown to be convergent to an optimal point of the considered optimization. Compared with other neurodynamic approaches, the presented neural network does not need any penalty parameters, and has lower model complexity. Furthermore, some additional assumptions in other existing related neural networks are also removed in this paper, such as the assumption that the objective function is lower bounded over the equality constraint set and so on. Finally, some numerical examples and an application in beamforming formulation are provided.