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Design and Analysis of Filter Trust-Region Algorithms for Unconstrained and Bound Constrained Optimization

Fatemi, Masoud | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42070 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Mahdavi Amiri, Nezameddin
  7. Abstract:
  8. Design, analysis and practical implementation of the filter trust-region algorithms are investigated. First, we introduce two filter trust-region algorithms for solving the unconstrained optimization problem. These algorithms belong to two different class of optimization algorithms: (1) The monotone class, and (2) The non-monotone class. We prove the global convergence of the sequence of the iterates generated by the new algorithms to the first and second order critical points. Then, we propose a filter trust-region algorithm for solving bound constrained optimization problems and show that the algorithm converges to a first order critical point. Moreover, we address some well known questions in the filter theory. These questions are about the possibility of the finiteness of the filter size and the existence of a correlation between problem dimension and the filter size. Here, for the first time, we introduce a new filter acceptance criterion and show the finiteness of the filter size. We also show a correlation between the problem dimension and the filter size and explain the difficulties with other existing filter criteria. Furthermore, we introduce a new mechanism to control the filter size. Finally, we implement the new algorithms with MATLAB codes and compare our obtained results on various test problems with the results of some other existing algorithms. Our numerical results confirm the efficiency of the new algorithms.
  9. Keywords:
  10. Unconstrainted Optimization ; Trust Region Subproblem ; Monotone Scheme ; Simple Bound Constrained Optimization ; Filter Methods ; Projected Gradient Method ; Non-Monotone Algorithm ; First Order Covergence ; Second Order Covergence

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