论文标题
MPRGP算法中的主动设置扩展策略
Active set expansion strategies in MPRGP algorithm
论文作者
论文摘要
本文调查了MPRGP算法可以采用的活动集合的策略。标准MPRGP扩展使用固定步长的自由梯度方向使用投影线搜索。这样的方案通常太慢，无法识别活动集，需要大量扩展。我们建议根据当前梯度使用自适应步长，以确保使用不同的基于梯度的搜索方向减少不受约束的成本函数。此外，我们还建议通过投影不受限制的最小化的最佳步骤来扩展活动集。数值实验证明了我们在两个基准测试基准上进行扩展步骤修改的好处 - TFETI解决了线性弹性的联系问题以及SVM类型的机器学习问题，均在Permon Toolbox中实现。
The paper investigates strategies for expansion of active set that can be employed by the MPRGP algorithm. The standard MPRGP expansion uses a projected line search in the free gradient direction with a fixed step length. Such a scheme is often too slow to identify the active set, requiring a large number of expansions. We propose to use adaptive step lengths based on the current gradient, which guarantees the decrease of the unconstrained cost function with different gradient-based search directions. Moreover, we also propose expanding the active set by projecting the optimal step for the unconstrained minimization. Numerical experiments demonstrate the benefits of our expansion step modifications on two benchmarks -- contact problem of linear elasticity solved by TFETI and machine learning problems of SVM type, both implemented in PERMON toolbox.
