Dissertation > Excellent graduate degree dissertation topics show

A Self-Correcting Geometry Wedge Trust Region Method in Derivative-Free Optimization

Author: ZhangLiang
Tutor: SunWenZuo
School: Nanjing Normal University
Course: Computational Mathematics
Keywords: Derivative-free optimization model-based methods unconstrained op-timization nonlinear complementarity problems wedge trust region methods self-correcting geometry
CLC: O224
Type: Master's thesis
Year: 2013
Downloads: 16
Quote: 0
Read: Download Dissertation

Abstract


In this paper, we study the new derivative-free method for solving unconstrained optimization problems and nonlinear complementarity problems.Derivative-free optimization is the method only using the function value and without any derivatives. So far, several efficient methods have been proposed for solving unconstrained optimization without derivatives. Here we consider trust re-gion methods based on interpolation models. The model function, i.e., the objective function of the subproblem, in each iteration is formed by interpolation and needs to satisfy some conditions to get a good iterative point. How to build appropriate models becomes a puzzle, so far there are three main methods:the geometry-improvement step, the wedge trust region method and the self-correcting geometry process.We propose a new self-correcting geometry process and combine the wedge trust region method, so we get a new derivative-free method for unconstrained problems. The new self-correcting geometry process adopts different updating strategies of in-terpolation point set and trust region radius to accelerate the convergence. We prove the new process also has the self-correcting property. What’s more, it can take the po-sition factor of the interpolation points and avoid the defects of only considering the position factor to combine the wedge trust region method. Numerical experiments in-dicate that the modified method is efficient. Under the general assumptions, we prove the convergence.In Chapter4, the new method is used to solve nonlinear complementarity prob-lems, through solving the transformed problems by merit function. If the regularity condition holds, then any accumulation point generated by the algorithm is the solu-tion of the NCR Numerical experiments show that our method works relatively better than the derivative-free descent method by J.S. Chen and S.H. Pan [1]. What’s more, the regularity condition is weaker than the convergence condition in derivative-free descent method.

Related Dissertations

  1. Some Studies on Memory Gradient Method for Unconstrained Optimization Problems,O224
  2. Some Studies on Numerical Algorithms for Complementarity Problems,O241
  3. Unconstrained optimization problems Adaptive Filter Trust Region Algorithm,O224
  4. Extended family of quasi-Newton method and its global convergence,O224
  5. Nonlinear Optimization Adaptive Trust Region Algorithm,O224
  6. Unconstrained optimization of the three non- monotone trust region algorithm,O224
  7. A Differential Equation Approach, Based on the Space Transformation of Square Function, to Complementarity Problems,O221
  8. Some Studies of the Grid-based Methods for Optimization Problems,O224
  9. Some Algorithms in Unconstrained Optimization,O241
  10. Unconstrained optimization problem for a class of non- monotone trust region algorithm,O224
  11. Variational inequality problem with unconstrained optimization problem,O224
  12. Some new nonlinear conjugate gradient method,O241
  13. Study on the Global Convergence of the Nonlinear Conjugate Gradient Method with SWP Line Search,O241
  14. A Modified PRP Formula for Unconstrained Optimization Problems,O224
  15. The Study of Filter Methods for Nonlinear Complementarity Problems,O224
  16. Study on the Parallel Algorithms for Optimization Problems,O224
  17. Theoretical Research on Reservoir Closed-loop Production Optimization,TE33
  18. Coevolutionary Numerical Optimization Algorithms and Their Applications,TP18
  19. Some Research about Nonmono-tone ODE-type Trust Region Method,O241.6
  20. Some Researching on Derivative-free Optimization Block Decomposition,O224
  21. Some Further Studies and Applications of IMPBOT Method,O224

CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Optimization of the mathematical theory
© 2012 www.DissertationTopic.Net  Mobile