-

 

 

 




Optimization Online





 

Iteration-complexity of an inexact proximal accelerated augmented Lagrangian method for solving linearly constrained smooth nonconvex composite optimization problems

Jefferson Melo (jefferson***at***ufg.br)
Renato Monteiro (monteiro***at***isye.gatech.edu)
Hairong Wang (hairongwhr***at***gatech.edu)

Abstract: This paper proposes and establishes the iteration-complexity of an inexact proximal accelerated augmented Lagrangian (IPAAL) method for solving linearly constrained smooth nonconvex composite optimization problems. Each IPAAL iteration consists of inexactly solving a proximal augmented Lagrangian subproblem by an accelerated composite gradient (ACG) method followed by a suitable Lagrange multiplier update. It is shown that IPAAL generates an approximate stationary solution in at most ${\cal O}(\log(1/\rho)/\rho^{3})$ ACG iterations, where $\rho>0$ is the given tolerance. It is also shown that the previous complexity bound can be sharpened to ${\cal O}(\log(1/\rho)/\rho^{2.5})$ under additional mildly stronger assumptions. The above bounds are derived assuming that the initial point is neither feasible nor the domain of the composite term of the objective function is bounded. Some preliminary numerical results are presented to illustrate the performance of the IPAAL method.

Keywords: Inexact proximal augmented Lagrangian methods, linearly constrained smooth nonconvex composite programs, accelerated first-order methods, iteration-complexity.

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation:

Download: [PDF]

Entry Submitted: 04/29/2020
Entry Accepted: 04/29/2020
Entry Last Modified: 06/14/2020

Modify/Update this entry


  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository

 

Submit
Update
Policies
Coordinator's Board
Classification Scheme
Credits
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society