Dissertation > Excellent graduate degree dissertation topics show

Filter Trust Region Algorithms for Unconstrained Optimization

Author: FuZuoZuo
Tutor: LiuTaoWen
School: Hunan University
Course: Operational Research and Cybernetics
Keywords: Unconstrained optimization trust region algorithm cautious filtertrust region algorithm filter trust region algorithm with four parameters globalconvergence superlinear convergence
CLC: O224
Type: Master's thesis
Year: 2012
Downloads: 17
Quote: 0
Read: Download Dissertation

Abstract


In this paper we present filter trust region algorithms for solving unconstrained op-timization problems. Fletcher and Leyfer proposed a filter method in1997to get overnumerical difculty when using improper penalty function for nonlinear constrainedoptimization problems. Filter technology has been widely applied to other optimiza-tion fields, due to its good convergence properties and numerical results. Such assolving nonlinear equations and unconstrained optimization problems,ones have pro-posed many efective algorithms based on filter technology. However, the efect of thesealgorithms greatly depend on the filter rules. In this paper we make further study thefilter structure and the relevant rules and then present two kinds of filter trust regionalgorithms: Cautious filter trust region algorithm and filter trust region algorithm withfour parameters.In Chapter1, we mainly introduce the development of the filter algorithm, do-mestic and international current situation analysis and its research significance of filteralgorithm. We introduces also the general trust region algorithm structure, definitionof general multidimensional filter and filter trust region algorithm.In Chapter2, we propose the definition of Cautious filter, which is a modificationof traditional filter, has reduced some flaws in the existing filter structure, such as somedifculties in the choice of parameter caused by the rigid filter rules. Meanwhile, weproposed the global convergence of cautious filter.In Chapter3, we present the filter trust region algorithm with four parameters,which is an extension of the filter trust region algorithm with two parameters. Thefilter technology with four parameters is more flexible for the choice of parameters andthe form is more diversified, and the filter technology with two parameters is a specialform of that. Therefore, it contains the advantage of the filter trust region algorithmwith two parameters. At last we prove the global and superlinear convergence of theproposed algorithm.In Chapter4, we perform the proposed algorithms. The numerical results showthat the proposed algorithms are practical efcient.

Related Dissertations

  1. Research on Some Nonlinear Conjugate Gradient Methods,O224
  2. Research on the Neutron Spectrum Unfolding Method Based on Trust Region Algorithm,O571.54
  3. An Efficlent Method for Solving Nenlinear Unconstrained Min-max Problem,O221.2
  4. Trust Region Algorithms Based on the Conic Model,O224
  5. Conditions for the Superlinear Convergence of Quasi-Newton Methods on Degenerate Solutions,O224
  6. A New Superlinearly Convergent Algorithm of Combining QP Subproblem with System of Linear Equations for Constrained Optimization,O241.6
  7. Research on the Filled Function Algorithms for Solving Nonlinear Global Optimization Problems,O224
  8. Smoothing Newton Method for Nonlinear Programming Problem and SQP-Filter Method for Constrained Minimax Problem,O221.2
  9. Trust-Region Algorithm Using Two-dimen-sional Subspace Technique with New Conic Model,O221.2
  10. Research on Nonmonotone Trust Region Algorithms for Nonlinear Optimization,O224
  11. A Nonmonotone Smoothing Newton Algorithm for Solving Zero-one Nonlinear Integer Programming Problems,O221.4
  12. A Modified SQP Algorithm for Nonlinearly Inequality Constrained Optimization,O224
  13. The Improvement of Nonlinear Conjugate Gradient Methods,O224
  14. Study of Several Algorithms for Solving Nonlinear Optimization Problems,O221.2
  15. The Study of Some Optimization Problems,O224
  16. A Modified Quasi-Newton Method and It’s Convergence,O224
  17. A New Class of Quasi-newton Algorithm and Its Convergence,O224
  18. Some Researches on the Algorithms for Solving a Class of Nonlinear Equations and Inequalities Problems,O224
  19. A RFTR Algorithm for Unconstrained Optimization,O224
  20. Some Studies on Memory Gradient Method for Unconstrained Optimization Problems,O224
  21. Research on the SQP Algorithm for Mathematical Programs with Equilibrium Constraints,O221

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