Paper Info
Title
Rate-Improved Inexact Augmented Lagrangian Method For Constrained Nonconvex Optimization
Abstract
First-order methods have been studied for nonlinear constrained optimization within the framework of the augmented Lagrangian method (ALM) or penalty method. We propose an improved inexact ALM (iALM) and conduct a unified analysis for nonconvex problems with either affine equality or nonconvex constraints. Under certain regularity conditions (that are also assumed by existing works), we show an (O) over tilde (epsilon(-5/2)) complexity result for a problem with a nonconvex objective and affine equality constraints and an (O) over tilde (epsilon(-3)) complexity result for a problem with a nonconvex objective and nonconvex constraints, where the complexity is measured by the number of first-order oracles to yield an epsilon-KKT solution. Both results are the best known. The same-order complexity results have been achieved by penalty methods. However, two different analysis techniques are used to obtain the results, and more importantly, the penalty methods generally perform significantly worse than iALM in practice. Our improved iALM and analysis close the gap between theory and practice. Numerical experiments on nonconvex problems with affine equality or nonconvex constraints are provided to demonstrate the effectiveness of our proposed method.
Year
Venue
DocType
2021
24TH INTERNATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE AND STATISTICS (AISTATS)
Conference
Volume
ISSN
Citations 
130
2640-3498
0
PageRank 
References 
Authors
0.34
0
5
Name
Order
Citations
PageRank
Zichong Li100.34
Pin-Yu Chen264674.59
Sijia Liu318142.37
Songtao Lu48419.52
Yangyang Xu549720.65