Dissertation > Excellent graduate degree dissertation topics show

Solving Quadratic Programming Problems Based on Neural Networks

Author: NiuJiuXiao
Tutor: LiuDeYou
School: Yanshan University
Course: Computational Mathematics
Keywords: projection neural network quadratic programming global stability saddlepoint theorem Lyapunov function sub-positive definite matrix
CLC: TP183
Type: Master's thesis
Year: 2012
Downloads: 36
Quote: 0
Read: Download Dissertation

Abstract


Optimization problems have been widely applied to scientific and engineering areas,such as signal and image processing, regression analysis and robot control, and so on.Artificial neural network, as a new subject, is considered to be a possible and verypromising approach to solve the optimization problems. Compared with traditionaloptimization algorithms, artificial neural network technique has more merits, such asfaster convergence rate, real-time control and hardware implementation, etc. In addition,due to the ubiquity of the time delay, it is necessary that the time delay is introduced intothe system in order to ensure the stability of the system. Therefore, the discussion of thedelayed project neural network for solving the optimization problems is of greattheoretical significance and practical value.In this thesis, by using saddle point theorem and projection theorem, we convert thequadratic programming problem into the problem of the projection equations. Based onthe projection equations and the delay theory, a delayed project neural network isconstructed, and the equilibrium point of network is equivalent to the optimal solution ofthe optimization problem. Then, the existence and uniqueness of the equilibrium point ofnetwork is proved based on saddle point theorem, and the global stability of the network isanalyzed. Finally, the simulations of several examples show the validity and thecorrectness of the network. Main content as follows:Firstly, we discuss a delayed project neural network for solving convex quadraticprogramming problems with linear constraints. By the variation-of-constants formula, theglobal exponential stability of the proposed neural network has been presented under someconditions.Secondly, we analysis a delayed project neural network for solving a class ofindefinite quadratic programming problems. By constructing a suitable Lyapunov-function,the global stability of the proposed neural network has been proved.Finally, we study a class of delayed project neural network for solving generalquadratic programming problems. By constructing a suitable Lyapunov-function and linear matrix inequality (LMI) methods, we get some sufficient conditions ensuring theglobal exponential stability of this network.

Related Dissertations

  1. Dynamics of an Ecological Stoichiometric Regrowth-Herbivore Model,O175
  2. The Research on the Algorithms of Some Large-scale Quadratic Programming,O221.2
  3. Quadratic programming and multi- objective planning of global optimality conditions,O221
  4. Reconfigurable Controller Design of Stratospheric Demonstrating Airship,V274
  5. Phased Array Radar Resource Optimization Management,TN958.92
  6. Qualitative Analysis on the Predator-prey Systems with Undercrowding Effect,O175.1
  7. Global Stability of Differential Equations with Piecewise Continuous Arguments and the Convergence of Exponential Runge-Kutta,O241.8
  8. The Transmission Dynamics of H1N1,O175
  9. Dynamical Systems and Attractors,O19
  10. The Study of Asymptotical Behaviors on Several Classes of Nonautonomous Difference Competitive System,O175.7
  11. The Space-time Dynamic Analysis in Predator-prey System with Holling Type Ⅲ Functional Response,O175.2
  12. Qualitative Analysis of Predator-prey System with the Holling Ⅳ Functional Response,O175
  13. Stability Analysis of Several Nonlinear Size-structured Population Systems,O211.3
  14. Complex Dynamic Behavior of Several Infectious Disease Models,O175
  15. Analysis and Research on Some Epidemical Models with Nonlinear Incidence,O242.1
  16. An SIR Epidemic Model,O242.1
  17. Study on Holling Predator-prey System Incorporating Prey Refuges and Harvesting,Q14
  18. A Qualitative Study of Simian Immunodeficiency Virus Model,O175.13
  19. Study of the Parallel Variable Distribution Algorithms of Quadratic Programming,O246
  20. Study of Some Algorithms for Two-Stage Stochastic Program and Its Applications,O221.5
  21. A Study on Population Dynamics in the Polluted Environment with Interference,O175

CLC: > Industrial Technology > Automation technology,computer technology > Automated basic theory > Artificial intelligence theory > Artificial Neural Networks and Computing
© 2012 www.DissertationTopic.Net  Mobile