论文标题
一种用于非线性优化的牛顿型活动集方法，并具有多面体约束
A Newton-Type Active Set Method for Nonlinear Optimization with Polyhedral Constraints
论文作者
论文摘要
提出了一种由多面体约束的大规模最小化的牛顿型活性集算法。该算法由一个梯度投影步骤组成，在约束矩阵的空空间中的二阶牛顿型步骤以及两个步骤之间分支的一组规则。我们表明，当主动约束线性独立并且二阶足够的最佳条件保持时，提出的方法渐近地采取了牛顿步骤。我们还表明，该方法在标准条件下具有二次收敛速率。介绍了数值实验，说明了最可爱的问题和特定类别的问题的算法的性能，该问题至关重要。
A Newton-type active set algorithm for large-scale minimization subject to polyhedral constraints is proposed. The algorithm consists of a gradient projection step, a second-order Newton-type step in the null space of the constraint matrix, and a set of rules for branching between the two steps. We show that the proposed method asymptotically takes the Newton step when the active constraints are linearly independent and a strong second-order sufficient optimality condition holds. We also show that the method has a quadratic rate of convergence under standard conditions. Numerical experiments are presented illustrating the performance of the algorithm on the CUTEst and on a specific class of problems for which finding second-order stationary points is critical.
