Adaptive augmented Lagrangian methods: algorithms and practical numerical experience

DOI10.1080/10556788.2015.1071813zbMath1339.49023arXiv1408.4500OpenAlexW1830979757MaRDI QIDQ2811487

Nicholas I. M. Gould, Daniel P. Robinson, Hao Jiang, Frank E. Curtis

Publication date: 10 June 2016

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.4500

zbMATH Keywords

large-scale optimizationnonlinear optimizationmatrix-free methodsnon-convex optimizationsteering methodsadaptive augmented Lagrangian methods

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Large-scale problems in mathematical programming (90C06) Nonlinear programming (90C30) Numerical methods involving duality (49M29) Numerical optimization and variational techniques (65K10) Numerical methods based on necessary conditions (49M05) Newton-type methods (49M15) Numerical methods based on nonlinear programming (49M37) Large-scale systems (93A15)

Related Items

Complexity of an inexact proximal-point penalty method for constrained smooth non-convex optimization, A Solver for Nonconvex Bound-Constrained Quadratic Optimization, An alternating trust region algorithm for distributed linearly constrained nonlinear programs, application to the optimal power flow problem, An adaptive sampling augmented Lagrangian method for stochastic optimization with deterministic constraints, Perturbed proximal primal-dual algorithm for nonconvex nonsmooth optimization, A new augmented Lagrangian method for equality constrained optimization with simple unconstrained subproblem, Adaptive augmented Lagrangian methods: algorithms and practical numerical experience, Complexity and performance of an Augmented Lagrangian algorithm

Uses Software

• LANCELOT
• Matlab
• AMPL
• PENNON

Cites Work

• Unnamed Item
• Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
• Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization
• A line search exact penalty method using steering rules
• An adaptive augmented Lagrangian method for large-scale constrained optimization
• On attraction of linearly constrained Lagrangian methods and of stabilized and quasi-Newton SQP methods to critical multipliers
• A dual algorithm for the solution of nonlinear variational problems via finite element approximation
• Automatic decrease of the penalty parameter in exact penalty function methods
• Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters.
• A numerical study of limited memory BFGS methods
• Numerical experiments with the Lancelot package (Release \(A\)) for large-scale nonlinear optimization
• CUTEst: a constrained and unconstrained testing environment with safe threads for mathematical optimization
• Augmented Lagrangian methods under the constant positive linear dependence constraint qualification
• Multiplier and gradient methods
• Adaptive augmented Lagrangian methods: algorithms and practical numerical experience
• Local Convergence of Exact and Inexact Augmented Lagrangian Methods under the Second-Order Sufficient Optimality Condition
• Real Analysis and Applications
• A Globally Convergent Augmented Lagrangian Algorithm for Optimization with General Constraints and Simple Bounds
• Improving ultimate convergence of an augmented Lagrangian method
• Steering exact penalty methods for nonlinear programming
• Global Convergence of a Class of Trust Region Algorithms for Optimization with Simple Bounds
• PENNON: A code for convex nonlinear and semidefinite programming
• Trust Region Methods
• Nonlinear stepsize control, trust regions and regularizations for unconstrained optimization
• GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization
• CUTEr and SifDec
• Practical Augmented Lagrangian Methods for Constrained Optimization
• Benchmarking optimization software with performance profiles.