一种非单调信赖域优化算法研究

一种非单调信赖域优化算法研究(任务书,开题报告,论文6500字)
摘  要
最优化理论与算法是数学学科中一个重要的分支，所研究的问题是在众多问题的解决方案中，讨论出一个最好的解决方案以及如何去寻找这类方案，从而最终得到一个解决问题的最优方案，并且最优化理论在工业、商业和军工等领域都得到了比较广泛的应用。而在最优化问题的求解方案中，信赖域算法因为具有很强的收敛性和自适应性,所以受到了非线性优化研究者们的极大重视。尤其是与单调的信赖域算法相比较，非单调的信赖域算法不仅减少了计算子问题的次数，而且避免了Maratos效应，在实际应用中具有非常重要的作用。
本论文着重研究解决非线性优化问题的非单调信赖域算法，针对基本信赖域算法中的实际下降量 进行调整，增加一个趋近于1的参数 ，放宽对信赖域半径的校正条件，得到一种新的非单调信赖域算法。所提出的新算法可以达到放大信赖域半径 的目的，即尽可能挣脱局部最优解的“牢笼”，使算法搜索到的局部最优解成为全局最优解。最终，理论证明该算法在适当条件下的全局收敛性，并且采用Matlab进行数值验证该算法的可行性与有效性。
关键词：最优化理论；非单调算法；新的信赖域算法；全局收敛性

Abstract
Optimization theory and algorithm is a mathematical discipline an important branch. The problem is studied in solution of many problems, discuss the best solution and how to find such solutions. Finally, get a solution to the problem of the optimal solution. Optimization theory in the field of engineering, physics, economics and management has been used widely. Because of strong convergence and adaptability, the trust region algorithm attracts the attention of nonlinear optimization researchers. Especially non-monotonic trust region algorithm, compared with the trust region algorithm for reducing the number of sub-problem calculation to avoid Maratos effect, plays an important role in practical applications.
The contents of this working paper focuses on the non-monotonic trust region algorithm for nonlinear optimization problems. Correcting the basic trust region algorithm actually decrease the amount of ,relax the trust region radius correction condition, to achieve the purpose of the trust region radius enlarge. That might jump out of ‘the cage’ local optima, optimal solution to make the search as much as possible to become a global optimal solution, thus proposes a new trust region algorithm. Finally, proving the global convergence of the algorithm with appropriate conditions, and using matlab numerical shows that the algorithm is feasible and effective.
Keywords：Optimization theory; non-monotonic algorithm; a new trust region algorithm; global convergence.
 
摘  要    3
第1章 绪论    1
1.1 线搜索方法    1
1.2 信赖域方法    2
1.2.1　信赖域方法的基本思想    2
1.2.2　信赖域方法的基本结构    2
1.3 信赖域方法国内外研究现状    4
1.4 非单调信赖域算法    5
1.5 本文主要研究内容    5
第2章 新的非单调信赖域方法    7
2.1 新的非单调信赖域算法    7
2.2 新算法的MATLAB数值实现    8
2.3 新算法的全局收敛性证明    9
结论    13
参考文献    14
致  谢    15