The Nelder-Mead (NM) method is a popular derivative-free optimization algorithm owing to its fast convergence and robustness. However, it is known that the method often fails to converge or costs a long time for a large-scale optimization. In the present study, the NM method has been improved using direct inversion in iterative subspace (DIIS). DIIS is a technique to accelerate an optimization method, extrapolating a better intermediate solution from linear-combination of the known ones. We compared runtimes of the new method (NM-DIIS) and the conventional NM method using unimodal test functions with various dimensions. The NM-DIIS method showed better results than the original NM on average when the dimension of the objective function is high. Long tails of the runtime distributions in the NM method have disappeared when DIIS was applied. DIIS has also been implemented in the quasi-gradient method, which is an improved version of the NM method developed by Pham et al. [IEEE Trans. Ind. Informatics, 7 (2011) 592]. The combined method also performed well especially in an upwardly convex test function. The present study proposes a practical optimization strategy and proves the versatility of DIIS.

Nelder-Mead（NM）方法由于其快速收敛性和鲁棒性而成为一种流行的无导数优化算法。但是，已知该方法通常无法收敛或花费大量时间进行大规模优化。在当前的研究中，NM方法已经在迭代子空间（DIIS）中使用直接反演得到了改进。DIIS是一种加速优化方法的技术，可以从已知组合的线性组合中推断出更好的中间解决方案。我们比较了新方法（NM-DIIS）和常规NM方法的运行时间，这些方法使用了具有各种尺寸的单峰测试函数。当目标函数的维数较大时，NM-DIIS方法的平均效果要优于原始NM。应用DIIS时，NM方法中运行时分布的长尾巴已经消失了。DIIS也已经用准梯度方法实现，它是Pham等人开发的NM方法的改进版本。[IEEE Trans。Ind.Informatics，7（2011）592]。组合方法也表现良好，尤其是在向上凸的测试功能中。本研究提出了一种实用的优化策略，并证明了DIIS的多功能性。