非单调楔形信赖域算法
发布时间：2018-11-18 13:34
【摘要】：楔形信赖域算法是求解无导数最优化问题的一类卓有成效的方法,它是在信赖域的基础上添加一个楔形约束,以此来确保插值模型的均衡性。而非单调技巧可以有效处理约束优化问题出现的martos效应,从而加速算法的收敛过程。特别对于目标函数具有陡峭狭长的谷底地带特点时是效果很好的一种计算方法。本文研究的是非单调楔形信赖域方法,通过充分了解上述两种方法的优缺点以后,为了更加快速的找到目标函数的最优解,引入了四种不同的非单调技巧,结合楔形约束,构造了利用上述方法的杂交算法。使得求解无导数最优化问题的插值模型算法更加完善,从而加快算法的运算效率。同时,本文进行了大量的数值实验,对四种非单调技巧进行了数值比较,数值结果表明,我们提出的改进的楔形信赖域算法普遍具有更高的计算效率。最后,本文还结合非单调技巧和几何校正的算法。几何校正是在产生新的迭代点时,用几何校正步来规划获得下一组插值点集。本文把这种方法加入到非单调楔形信赖域算法当中,更进一步保障了插值点的均衡性,提高了拟合插值模型的精确度,加快了算法的收敛速率。
[Abstract]:Wedge trust region algorithm is an effective method for solving derivative free optimization problems. It adds a wedge constraint to the trust region to ensure the equalization of the interpolation model. The non-monotone technique can effectively deal with the martos effect of constrained optimization problems, thus speeding up the convergence process of the algorithm. Especially when the objective function has the characteristic of steep and narrow valley floor, it is a good calculation method. In this paper, the nonmonotone wedge trust region method is studied. After fully understanding the advantages and disadvantages of the above two methods, in order to find the optimal solution of the objective function more quickly, four different nonmonotone techniques are introduced, which are combined with the wedge constraint. A hybrid algorithm using the above method is constructed. The interpolation model algorithm for solving Derivative-free optimization problem is improved, and the computational efficiency of the algorithm is accelerated. At the same time, a large number of numerical experiments are carried out to compare the four non-monotone techniques. The numerical results show that the improved wedge trust region algorithm is generally more efficient. Finally, this paper combines the non-monotone technique and geometric correction algorithm. Geometric correction is to obtain the next set of interpolation points by geometric correction step when generating new iterative points. In this paper, this method is added to the non-monotone wedge trust region algorithm, which further ensures the equalization of interpolation points, improves the accuracy of fitting interpolation model, and accelerates the convergence rate of the algorithm.
【学位授予单位】：河北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O224
本文编号：2340165
[Abstract]:Wedge trust region algorithm is an effective method for solving derivative free optimization problems. It adds a wedge constraint to the trust region to ensure the equalization of the interpolation model. The non-monotone technique can effectively deal with the martos effect of constrained optimization problems, thus speeding up the convergence process of the algorithm. Especially when the objective function has the characteristic of steep and narrow valley floor, it is a good calculation method. In this paper, the nonmonotone wedge trust region method is studied. After fully understanding the advantages and disadvantages of the above two methods, in order to find the optimal solution of the objective function more quickly, four different nonmonotone techniques are introduced, which are combined with the wedge constraint. A hybrid algorithm using the above method is constructed. The interpolation model algorithm for solving Derivative-free optimization problem is improved, and the computational efficiency of the algorithm is accelerated. At the same time, a large number of numerical experiments are carried out to compare the four non-monotone techniques. The numerical results show that the improved wedge trust region algorithm is generally more efficient. Finally, this paper combines the non-monotone technique and geometric correction algorithm. Geometric correction is to obtain the next set of interpolation points by geometric correction step when generating new iterative points. In this paper, this method is added to the non-monotone wedge trust region algorithm, which further ensures the equalization of interpolation points, improves the accuracy of fitting interpolation model, and accelerates the convergence rate of the algorithm.
【学位授予单位】：河北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O224
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1 许凤霞;周庆华;张亚蕊;耿燕;;关于楔形信赖域半径更新的两种方法[J];计算机工程与应用;2011年30期
相关硕士学位论文 前1条
1 吴元元;楔形信赖域算法的混合搜索方法[D];河北大学;2015年
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