Inexact-restoration algorithm for constrained optimization
Journal of Optimization Theory and Applications
Trust-region methods
On the Constant Positive Linear Dependence Condition and Its Application to SQP Methods
SIAM Journal on Optimization
A Globally Convergent Filter Method for Nonlinear Programming
SIAM Journal on Optimization
SIAM Journal on Optimization
On Augmented Lagrangian Methods with General Lower-Level Constraints
SIAM Journal on Optimization
On the convergence of the proximal algorithm for nonsmooth functions involving analytic features
Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
Low Order-Value Optimization and applications
Journal of Global Optimization
An Invitation to Tame Optimization
SIAM Journal on Optimization
SIAM Journal on Scientific Computing
Mathematics of Operations Research
Global minimization using an Augmented Lagrangian method with variable lower-level constraints
Mathematical Programming: Series A and B
Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization
Computational Optimization and Applications
Handling infeasibility in a large-scale nonlinear optimization algorithm
Numerical Algorithms
Approximate KKT points and a proximity measure for termination
Journal of Global Optimization
Journal of Global Optimization
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Necessary first-order sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constraint qualifications. A new condition of this type is introduced in the present paper. It is proved that a well-established augmented Lagrangian algorithm produces sequences whose limits satisfy the new condition. Practical consequences are discussed.