Analysis and implementation of a dual algorithm for constrained optimization
Journal of Optimization Theory and Applications
Algorithm 737: INTLIB—a portable Fortran 77 interval standard-function library
ACM Transactions on Mathematical Software (TOMS)
Trust-region methods
Numerical Recipes in FORTRAN: The Art of Scientific Computing
Numerical Recipes in FORTRAN: The Art of Scientific Computing
On Finitely Terminating Branch-and-Bound Algorithms for Some Global Optimization Problems
SIAM Journal on Optimization
Journal of Global Optimization
Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients
Computational Optimization and Applications
Convexification and Global Optimization in Continuous And
Convexification and Global Optimization in Continuous And
Canonical Duality Theory and Solutions to Constrained Nonconvex Quadratic Programming
Journal of Global Optimization
Numerical Comparison of Augmented Lagrangian Algorithms for Nonconvex Problems
Computational Optimization and Applications
A polyhedral branch-and-cut approach to global optimization
Mathematical Programming: Series A and B
A comparison of complete global optimization solvers
Mathematical Programming: Series A and B
A Global Optimization RLT-based Approach for Solving the Hard Clustering Problem
Journal of Global Optimization
A Global Optimization RLT-based Approach for Solving the Fuzzy Clustering Problem
Journal of Global Optimization
Complete Solutions and Extremality Criteria to Polynomial Optimization Problems
Journal of Global Optimization
An Exact Reformulation Algorithm for Large Nonconvex NLPs Involving Bilinear Terms
Journal of Global Optimization
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
Practical Bilevel Optimization: Algorithms and Applications (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Augmented Lagrangian methods under the constant positive linear dependence constraint qualification
Mathematical Programming: Series A and B
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
Improving ultimate convergence of an augmented Lagrangian method
Optimization Methods & Software - Dedicated to Professor Michael J.D. Powell on the occasion of his 70th birthday
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
A review of recent advances in global optimization
Journal of Global Optimization
A Progressive Barrier for Derivative-Free Nonlinear Programming
SIAM Journal on Optimization
Second-order negative-curvature methods for box-constrained and general constrained optimization
Computational Optimization and Applications
Global minimization using an Augmented Lagrangian method with variable lower-level constraints
Mathematical Programming: Series A and B
A New Sequential Optimality Condition for Constrained Optimization and Algorithmic Consequences
SIAM Journal on Optimization
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
The boundedness of penalty parameters in an augmented Lagrangian method with constrained subproblems
Optimization Methods & Software
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In a recent paper, Birgin, Floudas and Martínez introduced an augmented Lagrangian method for global optimization. In their approach, augmented Lagrangian subproblems are solved using the $$\alpha $$ BB method and convergence to global minimizers was obtained assuming feasibility of the original problem. In the present research, the algorithm mentioned above will be improved in several crucial aspects. On the one hand, feasibility of the problem will not be required. Possible infeasibility will be detected in finite time by the new algorithms and optimal infeasibility results will be proved. On the other hand, finite termination results that guarantee optimality and/or feasibility up to any required precision will be provided. An adaptive modification in which subproblem tolerances depend on current feasibility and complementarity will also be given. The adaptive algorithm allows the augmented Lagrangian subproblems to be solved without requiring unnecessary potentially high precisions in the intermediate steps of the method, which improves the overall efficiency. Experiments showing how the new algorithms and results are related to practical computations will be given.