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Neural Computing and Applications

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15-03-2018 | Original Article

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

Authors: Xinjian Huang, Baotong Cui

Published in: Neural Computing and Applications | Issue 10/2019

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Abstract

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.

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Title: A neural dynamic system for solving convex nonlinear optimization problems with hybrid constraints
Authors: Xinjian Huang
Baotong Cui
Publication date: 15-03-2018
Publisher: Springer London
Published in: Neural Computing and Applications / Issue 10/2019
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI: https://doi.org/10.1007/s00521-018-3422-4

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