A neural dynamic system for solving convex nonlinear optimization problems with hybrid constraints

作者：Huang, Xinjian^*; Cui, Baotong

来源：Neural Computing & Applications, 2019, 31(10): 6027-6038.

DOI：10.1007/s00521-018-3422-4

• Neural network
• Convex nonlinear optimization
• Fischer-Burmeister function
• Merit function
• Stability
• Convergent

This paper proposes a neural network model for solving convex nonlinear optimization problems (CNOP) with equality and inequality constraints, whose equilibrium point coincides with the solution of Karush-Kuhn-Tucker points of the CNOP. Based on equality transformation and a Fischer-Burmeister function, we first transform the CNOP into a unconstrained minimization problem via a merit function. Then, using the steepest descent method, the neural network is constructed. On the basis of the convex analysis theory, Lyapunov stability theory and LaSalle invariance principle, the proposed network is proved to be stable in the sense of Lyapunov and converges to the optimal solution of the CNOP. Moreover, the proposed neural network is proved to be exponentially stable. Comparing with the existing models, the proposed neural network has fewer variables and neurons, which makes circuit realization easier. Simulation results show the feasibility and efficiency of the proposed network.

• 出版日期2019-10
• 单位江南大学