论文标题
使用Marqlevalg的Marquardt-Levenberg算法使用Marqlevalg的强大而有效的优化
Robust and Efficient Optimization Using a Marquardt-Levenberg Algorithm with R Package marqLevAlg
论文作者
论文摘要
用于本地优化的经典通用算法R中的实现通常具有两个主要局限性，这些局限性在复杂问题上造成了困难：收敛标准太松，计算时间太长。通过依靠牛顿式算法（MLA），一种类似牛顿的方法，特别适合解决局部优化问题，我们提供了Marqlevalg套件的有效且通用的本地优化器，它（i）通过基于严格的融合量的距离来阻止对鞍点的相对距离的距离，以实现对目标的最大距离，以实现对鞍座的最大距离，以实现对目标的最大距离，以实现最大的距离，以实现对目标的最大距离，以实现对目标的最大距离，以实现对目标的最大距离，并以较小的距离的范围来预防距（ii）通过允许在每次迭代处进行并行计算来减少复杂设置中的计算时间。我们通过文献中的各种案例证明，我们的实施可靠，始终如一地达到最佳（即使其他优化器失败），并且通过对不同复杂统计模型的最大似然估计的示例，在复杂的设置中也大大减少了计算时间。
Implementations in R of classical general-purpose algorithms for local optimization generally have two major limitations which cause difficulties in applications to complex problems: too loose convergence criteria and too long calculation time. By relying on a Marquardt-Levenberg algorithm (MLA), a Newton-like method particularly robust for solving local optimization problems, we provide with marqLevAlg package an efficient and general-purpose local optimizer which (i) prevents convergence to saddle points by using a stringent convergence criterion based on the relative distance to minimum/maximum in addition to the stability of the parameters and of the objective function; and (ii) reduces the computation time in complex settings by allowing parallel calculations at each iteration. We demonstrate through a variety of cases from the literature that our implementation reliably and consistently reaches the optimum (even when other optimizers fail), and also largely reduces computational time in complex settings through the example of maximum likelihood estimation of different sophisticated statistical models.
