论文标题
一种自适应的超快速不精确的近端增强拉格朗日方法，用于光滑的非凸复合优化问题
An adaptive superfast inexact proximal augmented Lagrangian method for smooth nonconvex composite optimization problems
论文作者
论文摘要
这项工作提出了一种自适应超快速近端增强拉格朗日（AS-PAL）方法，用于求解线性约束的平滑非凸复合综合优化问题。每次迭代均不截然不见地解决了通过积极/自适应选择Prox Spitepsize获得的可能的非convex近端增强的Lagrangian（Al）子问题，目的是实质上改善其计算性能，然后通过完整的Lagrangian乘数更新。与其他AL方法相比，AS-PAL的主要优点是，它不需要与优化问题相关的参数知识（例如约束矩阵的大小，客观函数曲率等），因为它的适应性不仅在选择Prox步骤时，而且在使用至关重要的适应性富度梯度方面可以解决一个至关重要的综合梯度，以求解Proximble selve proximmem selve Al Subpros Al Subpros。通过广泛的计算实验证明，AS-PAL的速度和效率可以证明它可以比其他最新的惩罚和AL方法快十倍以上，尤其是在需要高精度的情况下。
This work presents an adaptive superfast proximal augmented Lagrangian (AS-PAL) method for solving linearly-constrained smooth nonconvex composite optimization problems. Each iteration of AS-PAL inexactly solves a possibly nonconvex proximal augmented Lagrangian (AL) subproblem obtained by an aggressive/adaptive choice of prox stepsize with the aim of substantially improving its computational performance followed by a full Lagrangian multiplier update. A major advantage of AS-PAL compared to other AL methods is that it requires no knowledge of parameters (e.g., size of constraint matrix, objective function curvatures, etc) associated with the optimization problem, due to its adaptive nature not only in choosing the prox stepsize but also in using a crucial adaptive accelerated composite gradient variant to solve the proximal AL subproblems. The speed and efficiency of AS-PAL is demonstrated through extensive computational experiments showing that it can solve many instances more than ten times faster than other state-of-the-art penalty and AL methods, particularly when high accuracy is required.
