Amini Keyvan, Kimiaei Morteza, Khotanlou Hassan
Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran.
Faculty of Mathematics, University of Vienna, Vienna, Austria.
Int J Comput Math. 2017 Dec 19;96(1):33-50. doi: 10.1080/00207160.2017.1413552. eCollection 2019.
In this paper, a new pattern search is proposed to solve the systems of nonlinear equations. We introduce a new non-monotone strategy which includes a convex combination of the maximum function of some preceding successful iterates and the current function. First, we produce a stronger non-monotone strategy in relation to the generated strategy by Gasparo [, Numer. Algorithms 28 (2001), pp. 171-186] whenever iterates are far away from the optimizer. Second, when iterates are near the optimizer, we produce a weaker non-monotone strategy with respect to the generated strategy by Ahookhosh and Amini [, Numer. Algorithms 59 (2012), pp. 523-540]. Third, whenever iterates are neither near the optimizer nor far away from it, we produce a medium non-monotone strategy which will be laid between the generated strategy by Gasparo [, Numer. Algorithms 28 (2001), pp. 171-186] and Ahookhosh and Amini [, Numer. Algorithms 59 (2012), pp. 523-540]. Reported are numerical results of the proposed algorithm for which the global convergence is established.
本文提出了一种新的模式搜索方法来求解非线性方程组。我们引入了一种新的非单调策略，该策略包括一些先前成功迭代的最大值函数与当前函数的凸组合。首先，每当迭代远离最优解时，相对于Gasparo [《数值算法》28 (2001)，第171 - 186页]所生成的策略，我们生成一种更强的非单调策略。其次，当迭代接近最优解时，相对于Ahookhosh和Amini [《数值算法》59 (2012)，第523 - 540页]所生成的策略，我们生成一种较弱的非单调策略。第三，每当迭代既不接近最优解也不远离最优解时，我们生成一种中等强度的非单调策略，该策略介于Gasparo [《数值算法》28 (2001)，第171 - 186页]以及Ahookhosh和Amini [《数值算法》59 (2012)，第523 - 540页]所生成的策略之间。文中报告了所提算法的数值结果，并证明了其全局收敛性。
