ABSTRACT 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 et al. [Nonmonotone algorithms for pattern search methods, 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 [An efficient nonmonotone trust-region method for unconstrained optimization, 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 et al. [Nonmonotone algorithms for pattern search methods, Numer. Algorithms 28 (2001), pp. 171–186] and Ahookhosh and Amini [An efficient nonmonotone trust-region method for unconstrained optimization, Numer. Algorithms 59 (2012), pp. 523–540]. Reported are numerical results of the proposed algorithm for which the global convergence is established.

中文翻译：

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非线性方程组的一种非单调模式搜索方法

摘要 在本文中，提出了一种新的模式搜索来求解非线性方程组。我们引入了一种新的非单调策略，其中包括一些先前成功迭代的最大函数和当前函数的凸组合。首先，相对于 Gasparo 等人的生成策略，我们产生了更强的非单调策略。[模式搜索方法的非单调算法，Numer。Algorithms 28 (2001), pp. 171–186] 每当迭代远离优化器时。其次，当迭代接近优化器时，相对于 Ahookhosh 和 Amini 生成的策略，我们产生了一个较弱的非单调策略[一种用于无约束优化的有效非单调信任区域方法，Numer。算法 59 (2012)，第 523-540 页]。第三，每当迭代既不靠近优化器也不远离优化器时，我们会生成一个中等非单调策略，该策略将放置在 Gasparo 等人生成的策略之间。[模式搜索方法的非单调算法，Numer。Algorithms 28 (2001), pp. 171–186] 以及 Ahookhosh 和 Amini [一种用于无约束优化的有效非单调信任区域方法，Numer。算法 59 (2012)，第 523-540 页]。报告了所提出的算法的数值结果，为其建立了全局收敛。算法 59 (2012)，第 523-540 页]。报告了所提出的算法的数值结果，为其建立了全局收敛。算法 59 (2012)，第 523-540 页]。报告了所提出的算法的数值结果，为其建立了全局收敛。