Augmented Lagrangian method is a well established tool for the solution of optimization problems with equality constraints. If combined with effective algorithms for the solution of bound constrained quadratic programming problems, it can solve efficiently very large problems with bound and linear equality constraints. The point of this paper is to show that the performance of the algorithm can be essentially improved by enhancing the information on the free set of current iterates into the reorthogonalization of equality constraints. The improvement is demonstrated on the numerical solution of a large problem arising from the application of domain decomposition methods to the solution of discretized elliptic variational inequality describing a variant of Hertz’s two-body contact problem.

增强拉格朗日方法是解决具有相等约束的优化问题的完善工具。如果与有效算法相结合来解决有界约束的二次规划问题，它可以有效地解决具有界和线性相等约束的非常大的问题。本文的要点是表明，通过将电流迭代的自由集上的信息增强到等式约束的重新正交化中，可以从根本上改善算法的性能。在域分解方法应用于描述赫兹两体接触问题的变体的离散椭圆变分不等式的解决方案中产生的一个大问题的数值解上，证明了这种改进。