Partially Strictly Monotone and Nonlinear Penalty Functions for Constrained Mathematical Programs
Computational Optimization and Applications
Some Results about Duality and Exact Penalization
Journal of Global Optimization
Further Study on Augmented Lagrangian Duality Theory
Journal of Global Optimization
Calmness and Exact Penalization in Vector Optimization with Cone Constraints
Computational Optimization and Applications
Lagrange Multipliers and Calmness Conditions of Order p
Mathematics of Operations Research
A geometric framework for nonconvex optimization duality using augmented lagrangian functions
Journal of Global Optimization
Convergence properties of augmented Lagrangian methods for constrained global optimization
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
Unified theory of augmented Lagrangian methods for constrained global optimization
Journal of Global Optimization
A new augmented Lagrangian approach to duality and exact penalization
Journal of Global Optimization
A primal dual modified subgradient algorithm with sharp Lagrangian
Journal of Global Optimization
Extended duality for nonlinear programming
Computational Optimization and Applications
Optimality Conditions via Exact Penalty Functions
SIAM Journal on Optimization
Augmented Lagrangian functions for constrained optimization problems
Journal of Global Optimization
Augmented Lagrangian function, non-quadratic growth condition and exact penalization
Operations Research Letters
Convergence of a class of penalty methods for constrained scalar set-valued optimization
Journal of Global Optimization
Existence of augmented Lagrange multipliers for cone constrained optimization problems
Journal of Global Optimization
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In this paper, the existence of an optimal path and its convergence to the optimal set of a primal problem of minimizing an extended real-valued function are established via a generalized augmented Lagrangian and corresponding generalized augmented Lagrangian problems, in which no convexity is imposed on the augmenting function. These results further imply a zero duality gap property between the primal problem and the generalized augmented Lagrangian dual problem. A necessary and sufficient condition for the exact penalty representation in the framework of a generalized augmented Lagrangian is obtained. In the context of constrained programs, we show that generalized augmented Lagrangians present a unified approach to several classes of exact penalization results. Some equivalences among exact penalization results are obtained.