Mathematical Programming: Series A and B
Exact penalty functions in constrained optimization
SIAM Journal on Control and Optimization
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
Zero duality gap for a class of nonconvex optimization problems
Journal of Optimization Theory and Applications
Local saddle points and convexification for nonconvex optimization problems
Journal of Optimization Theory and Applications
Saddle point generation in nonlinear nonconvex optimization
Proceedings of second world congress on Nonlinear analysts
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
Ill-Conditioning and Computational Error in Interior Methods for Nonlinear Programming
SIAM Journal on Optimization
Penalty/Barrier Multiplier Methods for Convex Programming Problems
SIAM Journal on Optimization
A Modified Barrier-Augmented Lagrangian Method for Constrained Minimization
Computational Optimization and Applications
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
Further Study on Augmented Lagrangian Duality Theory
Journal of Global Optimization
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
Saddle points of general augmented Lagrangians for constrained nonconvex optimization
Journal of Global Optimization
An approach to constrained global optimization based on exact penalty functions
Journal of Global Optimization
On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming
Journal of Global Optimization
Convergence of a class of penalty methods for constrained scalar set-valued optimization
Journal of Global Optimization
An artificial fish swarm algorithm based hyperbolic augmented Lagrangian method
Journal of Computational and Applied Mathematics
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We classify in this paper different augmented Lagrangian functions into three unified classes. Based on two unified formulations, we construct, respectively, two convergent augmented Lagrangian methods that do not require the global solvability of the Lagrangian relaxation and whose global convergence properties do not require the boundedness of the multiplier sequence and any constraint qualification. In particular, when the sequence of iteration points does not converge, we give a sufficient and necessary condition for the convergence of the objective value of the iteration points. We further derive two multiplier algorithms which require the same convergence condition and possess the same properties as the proposed convergent augmented Lagrangian methods. The existence of a global saddle point is crucial to guarantee the success of a dual search. We generalize in the second half of this paper the existence theorems for a global saddle point in the literature under the framework of the unified classes of augmented Lagrangian functions.