| A SUPERLINEARLY CONVERGENT TRUST REGION ALGORITHM FOR LC^1 CONSTRAINED OPTIMIZATION PROBLEMS |
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| 作者姓名： | 欧宜贵 侯定丕 |
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| 作者单位： | [1]DepartmentofAppliedMathematics,HainanUniversity,Haikou570228,China [2]DepartmentofMathematics,UniversityofScienceandTechnologyofChina,Hefei230026,China |
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| 摘 要： | In this paper, a new trust region algorithm for nonlinear equality constrained LC^1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subproblem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view.
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| 关 键 词： | LC^1最优化 非线性平等约束 置信预算法 二次规划 超线性收敛 |
| 收稿时间： | 13 September 2001 |
A SUPERLINEARLY CONVERGENT TRUST REGION ALGORITHM FOR LC1 CONSTRAINED OPTIMIZATION PROBLEMS |
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| Ou Yigui,Hou Dingpi.A SUPERLINEARLY CONVERGENT TRUST REGION ALGORITHM FOR LC^1 CONSTRAINED OPTIMIZATION PROBLEMS[J].Acta Mathematica Scientia,2005,25(1):67-80. |
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| Authors: | Ou Yigui Hou Dingpi |
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| Institution: | 1. School of Transportation, Nantong University, Nantong, 226019, PR China;2. School of Mathematical Sciences, Soochow University, Suzhou, 215006, PR China;3. School of Urban Rail Transportation, Soochow University, Suzhou, 215006, PR China |
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| Abstract: | In this paper, a new trust region algorithm for nonlinear equality constrained LC1 optimization problems is given. It obtains a search direction at each iteration not by solving a quadratic programming subproblem with a trust region bound, but by solving a system of linear equations. Since the computational complexity of a QP-Problem is in general much larger than that of a system of linear equations, this method proposed in this paper may reduce the computational complexity and hence improve computational efficiency. Furthermore, it is proved under appropriate assumptions that this algorithm is globally and super-linearly convergent to a solution of the original problem. Some numerical examples are reported, showing the proposed algorithm can be beneficial from a computational point of view. |
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| Keywords: | LC1 optimization ODE methods trust region methods superlinear convegence |
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