论文标题
分段线性界面复合优化问题的增强拉格朗日方法的局部收敛分析
Local Convergence Analysis of Augmented Lagrangian Methods for Piecewise Linear-Quadratic Composite Optimization Problems
论文作者
论文摘要
二阶足够的局部最优条件一直在优化算法的局部收敛分析中发挥重要作用。在本文中，我们证明，仅这种条件就足以证明原始偶序序列的线性收敛是合理的，这是由增强的拉格朗日方法生成的，即使在此类问题中的拉格兰格乘法器中，也不唯一。此外，我们在此类的复合优化问题中建立了二阶足够条件与增强拉格朗日问题的二次生长条件之间的等效性。
Second-order sufficient conditions for local optimality have been playing an important role in local convergence analysis of optimization algorithms. In this paper, we demonstrate that this condition alone suffices to justify the linear convergence of the primal-dual sequence, generated by the augmented Lagrangian method for piecewise linear-quadratic composite optimization problems, even when the Lagrange multiplier in this class of problems is not unique. Furthermore, we establish the equivalence between the second-order sufficient condition and the quadratic growth condition of the augmented Lagrangian problem for this class of composite optimization problems.
