An Accelerated Inexact Dampened Augmented Lagrangian Method for Linearly-Constrained Nonconvex Composite Optimization Problems

Abstract

This paper proposes and analyzes an accelerated inexact dampened augmented Lagrangian (AIDAL) method for solving linearly-constrained nonconvex composite optimization problems. Each iteration of the AIDAL method consists of: (i) inexactly solving a dampened proximal augmented Lagrangian (AL) subproblem by calling an accelerated composite gradient (ACG) subroutine; (ii) applying a dampened and under-relaxed Lagrange multiplier update; and (iii) using a novel test to check whether the penalty parameter of the AL function should be increased. Under several mild assumptions involving the dampening factor and the under-relaxation constant, it is shown that the AIDAL method generates an approximate stationary point of the constrained problem in $\mathcal{O}({\epsilon }^{-5/2}\log {\epsilon }^{-1})$ iterations of the ACG subroutine, for a given tolerance $\epsilon >0$. Numerical experiments are also given to show the computational efficiency of the proposed method.

References in corpus (12)

• Convergence rate bounds for a proximal ADMM with over-relaxation stepsize parameter for solving nonconvex linearly constrained problems
• Sparse PCA with Oracle Property
• An Inexact Augmented Lagrangian Framework for Nonconvex Optimization with Nonlinear Constraints
• An accelerated inexact proximal point method for solving nonconvex-concave min-max problems
• Inexact Proximal-Point Penalty Methods for Constrained Non-Convex Optimization
• Iteration complexity of first-order augmented Lagrangian methods for convex conic programming
• Iteration-complexity of an inexact proximal accelerated augmented Lagrangian method for solving linearly constrained smooth nonconvex composite optimization problems
• A global dual error bound and its application to the analysis of linearly constrained nonconvex optimization
• Rate-improved Inexact Augmented Lagrangian Method for Constrained Nonconvex Optimization
• A Doubly Accelerated Inexact Proximal Point Method for Nonconvex Composite Optimization Problems
• Accelerated Inexact First-Order Methods for Solving Nonconvex Composite Optimization Problems
• On the non-ergodic convergence rate of an inexact augmented Lagrangian framework for composite convex programming

Cited by in corpus (1)

• Global Complexity Bound of a Proximal ADMM for Linearly-Constrained Nonseperable Nonconvex Composite Programming