【摘要】：楔形信賴域算法是求解無導(dǎo)數(shù)最優(yōu)化問題的一類卓有成效的方法,它是在信賴域的基礎(chǔ)上添加一個楔形約束,以此來確保插值模型的均衡性。而非單調(diào)技巧可以有效處理約束優(yōu)化問題出現(xiàn)的martos效應(yīng),從而加速算法的收斂過程。特別對于目標(biāo)函數(shù)具有陡峭狹長的谷底地帶特點時是效果很好的一種計算方法。本文研究的是非單調(diào)楔形信賴域方法,通過充分了解上述兩種方法的優(yōu)缺點以后,為了更加快速的找到目標(biāo)函數(shù)的最優(yōu)解,引入了四種不同的非單調(diào)技巧,結(jié)合楔形約束,構(gòu)造了利用上述方法的雜交算法。使得求解無導(dǎo)數(shù)最優(yōu)化問題的插值模型算法更加完善,從而加快算法的運算效率。同時,本文進行了大量的數(shù)值實驗,對四種非單調(diào)技巧進行了數(shù)值比較,數(shù)值結(jié)果表明,我們提出的改進的楔形信賴域算法普遍具有更高的計算效率。最后,本文還結(jié)合非單調(diào)技巧和幾何校正的算法。幾何校正是在產(chǎn)生新的迭代點時,用幾何校正步來規(guī)劃獲得下一組插值點集。本文把這種方法加入到非單調(diào)楔形信賴域算法當(dāng)中,更進一步保障了插值點的均衡性,提高了擬合插值模型的精確度,加快了算法的收斂速率。
[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.
【學(xué)位授予單位】：河北大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O224

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本文編號：2340165