Implementation of a Retrospective Trust-Region Method for Unconstrained Optimization

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Rezapour, Mostafa | 2012

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 42480 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Amiri, Nezamoddin
Abstract:
We explain a new trust region algorithm for solving unconstrained optimization problems where the redius update is computed using the model information at the current iterate rather than at the preceding one, recently proposed by Bastin, Malmedy, Mouffe, Toint and Tomanos. Then we discuss a modification mixing the concepts of nonmonotone trust region, line search and internal doubling. We use line search to finds a point that satisfies the Wolfe conditions. After that, we explain a new trust region algorithm for solving unconstrained optimization problems where simultaneously satisfies the quasi-Newton condition at each iteration and maintains a positive-definite approximation to the Hessian of the objective function, recently proposed by E. Michael Gertz. Global convergence to first- and second-order critical points is shown under classical assumptions. Finally, we implement the algorithms and test the programs on various problems. The results indeed show the effectiveness of the algorithms
Keywords:
Line Search ; Trust Region ; Nonmonotone Trust Region Method ; Unconstrained Minimization ; Internal Doubling Trust Region

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