Dual techniques for constrained optimization
Journal of Optimization Theory and Applications
SIAM Journal on Numerical Analysis
Lagrange multipliers and optimality
SIAM Review
Modified barrier functions (theory and methods)
Mathematical Programming: Series A and B
On the convergence of the exponential multiplier method for convex programming
Mathematical Programming: Series A and B
Journal of Optimization Theory and Applications
Zero duality gap for a class of nonconvex optimization problems
Journal of Optimization Theory and Applications
Mathematical Programming: Series A and B
On the twice differentiable cubic augmented Lagrangian
Journal of Optimization Theory and Applications
Local saddle points and convexification for nonconvex optimization problems
Journal of Optimization Theory and Applications
Local convexification of the Lagrangian function in nonconvex optimization
Journal of Optimization Theory and Applications
An Augmented Lagrangian Function with Improved Exactness Properties
SIAM Journal on Optimization
A Nonlinear Lagrangian Approach to Constrained Optimization Problems
SIAM Journal on Optimization
Decreasing Functions with Applications to Penalization
SIAM Journal on Optimization
Existence of a Saddle Point in Nonconvex Constrained Optimization
Journal of Global Optimization
The Zero Duality Gap Property and Lower Semicontinuity of the Perturbation Function
Mathematics of Operations Research
A Unified Augmented Lagrangian Approach to Duality and Exact Penalization
Mathematics of Operations Research
Numerical Comparison of Augmented Lagrangian Algorithms for Nonconvex Problems
Computational Optimization and Applications
On Saddle Points of Augmented Lagrangians for Constrained Nonconvex Optimization
SIAM Journal on Optimization
Primal-dual nonlinear rescaling method with dynamic scaling parameter update
Mathematical Programming: Series A and B
Augmented Lagrangian methods under the constant positive linear dependence constraint qualification
Mathematical Programming: Series A and B
Abstract Convexity and Augmented Lagrangians
SIAM Journal on Optimization
On the Convergence of Augmented Lagrangian Methods for Constrained Global Optimization
SIAM Journal on Optimization
On Augmented Lagrangian Methods with General Lower-Level Constraints
SIAM Journal on Optimization
An augmented Lagrangian fish swarm based method for global optimization
Journal of Computational and Applied Mathematics
Augmented Lagrangian functions for constrained optimization problems
Journal of Global Optimization
Saddle points of general augmented Lagrangians for constrained nonconvex optimization
Journal of Global Optimization
On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming
Journal of Global Optimization
An artificial fish swarm algorithm based hyperbolic augmented Lagrangian method
Journal of Computational and Applied Mathematics
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In this paper, we present new convergence properties of the primal-dual methods based on Rockafellar and Wets's augmented Lagrangian function for inequality constrained global optimization problems. Four different algorithmic strategies are considered to circumvent the boundedness condition of the multipliers in the convergence analysis for basic primal-dual method. We first show that under weaker conditions, the augmented Lagrangian method using safeguarding strategy converges to a global optimal solution of the original problem. The convergence properties of the augmented Lagrangian method using conditional multiplier updating rule is then presented. We also investigate the use of penalty parameter updating criteria and normalization of the multipliers in augmented Lagrangian methods. Finally, we present some preliminary numerical results for the four modified augmented Lagrangian methods.