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.
翻译:传统通用算法用于地方优化的实施一般有两大限制,对复杂问题的应用造成困难:过于松散的趋同标准和过长的计算时间。 依靠马尔夸特-莱文贝格算法(MLA)(MLA),一种对解决地方优化问题特别有力的牛顿式方法,我们向MarqLevAlg提供了一套高效和通用的本地优化软件,该软件包(i) 使用严格的趋同标准,在参数和目标功能的稳定性之外,以离最低/最高点的相对距离为基础,防止交汇点;以及(ii) 通过允许在每种迭代进行平行计算,缩短复杂环境下的计算时间。 我们通过文献中的各种案例表明,我们的执行情况可靠和一致地达到了最佳水平(即使其他优化器不成功),并且通过对不同的复杂统计模型进行最大可能性的估计,在很大程度上减少了复杂环境下的计算时间。