Adaptive augmented Lagrangian methods: algorithms and practical numerical experience
Adaptive augmented Lagrangian methods: algorithms and practical numerical experience
复制标题
DOI：
10.1080/10556788.2015.1071813
复制
发表时间：
2014-08
影响因子：
2.2
通讯作者：
Frank E. Curtis;N. Gould;Hao Jiang;Daniel P. Robinson
中科院分区：
文献类型：
--
作者：
Frank E. Curtis;N. Gould;Hao Jiang;Daniel P. Robinson
在本文中，我们考虑增广拉格朗日（AL）算法来解决大规模非线性优化问题，这些问题执行自适应策略来更新惩罚参数。我们的工作受到Curtis等人最近提出的自适应人工智能信任域方法的激励。[大规模约束优化的自适应增强拉格朗日方法，数学。]程序，152 (2015),pp. 201-245。本文的第一个重点是采用线搜索而不是信任域策略的方法的新变体，其中线搜索策略的关键算法特征是使用人工智能函数的凸分段二次模型来计算搜索方向。我们证明了我们的线搜索算法的全局收敛性保证与先前提出的信赖域方法相当。本文的第二个重点是Matlab软件中线搜索和信任域算法变体的实际性能，以及纳入Lancelot软件的自适应惩罚参数更新策略的实际性能。我们对CUTEst和COPS集合中的问题以及与最佳功率流相关的挑战性测试问题测试了这些方法。我们的数值经验表明，自适应算法在效率和可靠性方面优于传统的人工智能方法。与传统的人工智能算法一样，自适应方法是无矩阵的，因此代表了解决大规模问题的可行选择。
In this paper, we consider augmented Lagrangian (AL) algorithms for solving large-scale nonlinear optimization problems that execute adaptive strategies for updating the penalty parameter. Our work is motivated by the recently proposed adaptive AL trust region method by Curtis et al. [An adaptive augmented Lagrangian method for large-scale constrained optimization, Math. Program. 152 (2015), pp. 201–245.]. The first focal point of this paper is a new variant of the approach that employs a line search rather than a trust region strategy, where a critical algorithmic feature for the line search strategy is the use of convexified piecewise quadratic models of the AL function for computing the search directions. We prove global convergence guarantees for our line search algorithm that are on par with those for the previously proposed trust region method. A second focal point of this paper is the practical performance of the line search and trust region algorithm variants in Matlab software, as well as that of an adaptive penalty parameter updating strategy incorporated into the Lancelot software. We test these methods on problems from the CUTEst and COPS collections, as well as on challenging test problems related to optimal power flow. Our numerical experience suggests that the adaptive algorithms outperform traditional AL methods in terms of efficiency and reliability. As with traditional AL algorithms, the adaptive methods are matrix-free and thus represent a viable option for solving large-scale problems.