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| 摘要: |
| 本文研究了无约束最优化问题的基于锥模型的自适应信赖域算法.利用理论分析得到一个新的自适应信赖域半径.算法在每步迭代中以变化的速率、当前迭代点的信息以及水平向量信息调节信赖域半径的大小.从理论上证明了新算法的全局收敛性和Q-二阶收敛性.用数值试验验证了新算法的有效性.推广了已有的自适应信赖域算法的可行性和有效性. |
| 关键词: 无约束最优化 信赖域方法 锥模型 自适应 收敛性 |
| DOI： |
| 分类号:0224.2 |
| 基金项目:国家自然科学基金(11061011);广西自然科学基金(2011GXNSFA018138);重庆文理学院课题(Y2013sc42). |
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| A SELF-ADAPIVE TRUST REGION METHOD AND ITS CONVERGENCE WITH THE CONIC MODEL |
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FENG Lin,DUAN Fu-jian
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| Abstract: |
| In this paper, we study a self-adaptive trust region algorithm based on the conic model for unconstrained optimization problems. A new self-adaptive trust region radius is produced under theoretical analysis. At each iterative, the trust region radius is updated at a variable rate, the information at the current point and the level vector information. We analyze the global convergence and Q-quadratic convergence of the new method. Numerical results are also presented to test the efficiency of the new method which extend the application and efficiency of self-adaptive trust region algorithms. |
| Key words: unconstrained optimization trust region method conic model self-adaptive convergence |
