Dissertation > Excellent graduate degree dissertation topics show

Trust-Region Algorithm Using Two-dimen-sional Subspace Technique with New Conic Model

Author: WuXiaoLi
Tutor: NiQin
School: Nanjing University of Aeronautics and Astronautics
Course: Operational Research and Cybernetics
Keywords: two-dimensional subspace technique conic model trust region method unconstrained optimization global convergence
CLC: O221.2
Type: Master's thesis
Year: 2009
Downloads: 26
Quote: 0
Read: Download Dissertation

Abstract


The trust-region methods are effective for solving nonlinear optimization problems, they are blessed with both strong convergence properties in theory and a good result in computing. Two-dimensional subspace technique means that we can search a direction or get a trial step in some two-dimension space, its applications have the advantage of reducing both computation cost and memory size. So it has very good properties to combine two-dimensional subspace technique with trust-region methods, this idea has been applied to quadratic model, and good results have been achieved. But if the objective function has strong non-quadratic behavior or its curvature changes severely, the quadratic model methods often produce a poor prediction of the minimization of the function while the conic model one may serve better. Consequently, two-dimensional subspace algorithm with quadratic model is extended to conic model, and a good result is obtained.This paper applies two-dimensional subspace technique to trust-region subproblem involving a conic model, and proposes two-dimensional subspace trust-region subproblem with conic model. In addition, the two-dimension subspace trust-region algorithm with new conic model is established for solving unconstrained optimization problems. The dissertation consists of five chapters. Chapters 1 and 2 are introductory. They contains some preparatory materials of trust region method, the conic model ,subspace technique and the dogleg method. In Chapter 3, we first introduce two-dimensional subspace trust-region subproblem with quadratic model ,then we convert trust-region subproblem with conic model into a two dimension case, and give the detailed process and the algorithm. Moreover, we have proved the decreasing property of this algorithm. In Chapter 4 we solve the unconstrained optimization problem by the result got in Chapter 3, and propose the two-dimensional subspace trust-region algorithm with conic model and prove its global convergence. Finally, in Chapter 5, numerical experiment results are given.

Related Dissertations

  1. Trust Region Algorithms Based on the Conic Model,O224
  2. Unconstrained Nonlinear Conjugate Gradient Method,O224
  3. Studies on Efficient Algorithms for Finite-Dimensional Variational Inequality and Complementarity Problems,O242.23
  4. Study of the Algorithm for Nonlinear Bilevel Programming,O221.2
  5. Research on the Filled Function Algorithms for Solving Nonlinear Global Optimization Problems,O224
  6. Smoothing Newton Method for Nonlinear Programming Problem and SQP-Filter Method for Constrained Minimax Problem,O221.2
  7. Theory and Algorithm Study of Two Kinds of Nonlinear Bilevel Programming,O221.2
  8. Geometric Programming Based on Trust Region Algorithm,O221
  9. Trust Region Method of New Conic Model for Nonlinearly Equality Constrained Optimization,O221.2
  10. A Modified SQP Algorithm for Nonlinearly Inequality Constrained Optimization,O224
  11. The Improvement of Nonlinear Conjugate Gradient Methods,O224
  12. Study of Several Algorithms for Solving Nonlinear Optimization Problems,O221.2
  13. The Study of Some Optimization Problems,O224
  14. Two New Nonmonotone Line Search Methods,O224
  15. A Modified Quasi-Newton Method and It’s Convergence,O224
  16. A New Class of Quasi-newton Algorithm and Its Convergence,O224
  17. Improved genetic algorithm in nonlinear equations,O241.7
  18. Some Researches on the Semi-smoothing Asymptotically Newton Method for Complementarity Problems,O241.6
  19. Research on the Superlinearly Convergent Algorithms for Optimization with Equilibrium Constraints,O221.2
  20. A Class of Modified BFGS Trust Region Method,O224
  21. Research on a Method of Moving Asymptotes for Solving Unconstrained Optimization Problems,O224

CLC: > Mathematical sciences and chemical > Mathematics > Operations Research > Planning Theory ( mathematical programming) > Nonlinear Programming
© 2012 www.DissertationTopic.Net  Mobile