| A SPARSE SUBSPACE TRUNCATED NEWTON METHOD FOR LARGE-SCALE BOUND CONSTRAINED NONLINEAR OPTIMIZATION |
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| 作者姓名： | 倪勤 |
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| 作者单位： | NiQin College of Science，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，PRC. |
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| 基金项目： | The research was supported by the State Education Grant for Retumed Scholars |
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| 摘 要： | In this paper we report a sparse truncated Newton algorithm for handling large-scale simple bound nonlinear constrained minimixation problem. The truncated Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At each iterative level, the search direction consists of three parts, one of which is a subspace truncated Newton direction, the other two are subspace gradient and modified gradient directions. The subspace truncated Newton direction is obtained by solving a sparse system of linear equations. The global convergence and quadratic convergence rate of the algorithm are proved and some numerical tests are given.
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A SPARSE SUBSPACE TRUNCATED NEWTON METHOD FOR LARGE-SCALE BOUND CONSTRAINED NONLINEAR OPTIMIZATION |
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| NiQin College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing ,PRC..A SPARSE SUBSPACE TRUNCATED NEWTON METHOD FOR LARGE-SCALE BOUND CONSTRAINED NONLINEAR OPTIMIZATION[J].Numerical Mathematics A Journal of Chinese Universities English Series,1997(1). |
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| Authors: | NiQin College of Science Nanjing University of Aeronautics and Astronautics Nanjing PRC |
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| Institution: | NiQin College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,PRC. |
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| Abstract: | In this paper we report a sparse truncated Newton algorithm for handling large-scale simple bound nonlinear constrained minimization problem. The truncated Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. At each iterative level, the search direction consists of three parts, one of which is a subspace truncated Newton direction, the other two are subspace gradient and modified gradient directions. The subspace truncated Newton direction is obtained by solving a sparse system of linear equations. The global convergence and quadratic convergence rate of the algorithm are proved and some numerical tests are given. |
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| Keywords: | The truncated Newton method large-scale sparse problems bound constrained nonlinear optimization |
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