The Algorithms Of Two Optimization Problems Based On Networks

With the rapid development of computer hardware and network technology,various kinds of optimization problems in wireless communication,sensor network,automatic control,smart grid,and machine learning,and other fields have been widely applied.The design of efficien-t numerical algorithms for these optimization problems by using neural network model and a multiagent system has become a hot issue in the field of artificial intelligence research.This dis-sertation mainly studies the exponential stability of a class of full range cellular neural network models,the neurodynamic optimization algorithms for a class of complex-variables optimiza-tion problems,and the adaptive algorithms for a class of distributed optimization problems.The main contents of this dissertation are as follows:1.In Chapter 1,the research status of neural network,neurodynamic optimization and the consistency of multiagent system is briefly summarized and introduced.The research status and significance about the exponential stability of the full range cellular neural network,the complex-valued neural network model solving the complex-variables optimization problem and the consistent optimization algorithm for the multi-agent system the distribution optimization problem are discussed.2.In Chapter 2,some necessary preliminaries are introduced,including nonsmooth analy-sis,differential inclusions and algebraic graph theory.3.In Chapter 3,the dynamic behaviors of a class of full range cellular neural networks with variable coefficients and varying-time delays are considered.Firstly,an improved full range cellular neural network model is proposed,and the existence and uniqueness of its solution are proved based on the theory of differential inclusions and set-valued mapping.Then,by using Hardy inequality,matrix analysis and Lyapunov function method,the global exponential stability criteria of the model are established.4.In Chapter 4,a neural network model based on differential inclusion is proposed to solve the complex-variables optimization problems.The proposed model introduces Tikhonov regular term to replace the penalty parameters,and uses the penalty method to deal with affine equality constraints to avoid the calculation of projection matrix.Then,it is proved that any initial state of the model can reach the feasible region of the optimization problem in finite time.Furthermore,it is obtained that any initial state can asymptotically converge to the optimal solution set.5.In Chapter 5,two adaptive algorithms are designed to solve the problem of distributed convex optimization from the viewpoint of edges and nodes.The algorithms are designed based on the generalized linear multi-agent system,and use only the information of each agent and its neighbor nodes to reach the optimal solution cooperatively.The damping term is introduced into the adaptive law of the algorithms,which changes the characteristic of monotone increase of adaptive law and makes the proposed algorithms more robust in the face of input disturbance.