### Citations

804 | Constrained Optimization and Lagrange Multipliers Method - BERTSEKAS - 1982 |

478 | Numerical Methods for Unconstrained Optimization and Nonlinear Equations - Schnabel - 1996 |

377 | Benchmarking optimization software with performance profiles
- Dolan, Moré
(Show Context)
Citation Context ... on standard and degenerate problems. Figure 1 summarizes the numerical results of SPDOPT-AL, SPDOPT-QP-1 and SPDOPT-QP-2 on the set of standard and degenerate problems by the performance profiles of =-=[12]-=- on the number of function evaluations. For τ ≥ 0, ρs(τ) is the fraction of problems for which the performance of a given solver is within a factor 2τ of the best one. These performance profiles allow... |

293 | On the implementation of an interiorpoint filter line-search algorithm for large-scale nonlinear programming - Wächter, Biegler |

201 | P.L.: Trust-region methods
- Conn, Gould, et al.
- 2000
(Show Context)
Citation Context ... means that a quadratic rate of convergence can be expected by an appropriate updating strategy of the parameters σ and λ. Augmented Lagrangian methods have been fully studied in the past, see, e.g., =-=[5, 10]-=-. Some efficient software like LANCELOT-A [8, 9] and ALGENCAN [1, 2, 6] have been developed. There is a recent revival of algorithms based on an augmented Lagrangian formulation in the context of prim... |

110 |
P.L.: LANCELOT: a Fortran package for large-scale nonlinear optimization (release A). Springer series in computational mathematics
- Conn, Gould, et al.
- 1992
(Show Context)
Citation Context ...e expected by an appropriate updating strategy of the parameters σ and λ. Augmented Lagrangian methods have been fully studied in the past, see, e.g., [5, 10]. Some efficient software like LANCELOT-A =-=[8, 9]-=- and ALGENCAN [1, 2, 6] have been developed. There is a recent revival of algorithms based on an augmented Lagrangian formulation in the context of primal-dual methods [16, 18] or sequential quadratic... |

92 | A Globally Convergent Augmented Lagrangian Algorithm for Optimization With General Constraints and Simple Bounds
- Conn, Gould, et al.
- 1991
(Show Context)
Citation Context ...e expected by an appropriate updating strategy of the parameters σ and λ. Augmented Lagrangian methods have been fully studied in the past, see, e.g., [5, 10]. Some efficient software like LANCELOT-A =-=[8, 9]-=- and ALGENCAN [1, 2, 6] have been developed. There is a recent revival of algorithms based on an augmented Lagrangian formulation in the context of primal-dual methods [16, 18] or sequential quadratic... |

84 | On augmented lagrangian methods with general lower-level constraints
- Andreani, Birgin, et al.
(Show Context)
Citation Context ...ropriate updating strategy of the parameters σ and λ. Augmented Lagrangian methods have been fully studied in the past, see, e.g., [5, 10]. Some efficient software like LANCELOT-A [8, 9] and ALGENCAN =-=[1, 2, 6]-=- have been developed. There is a recent revival of algorithms based on an augmented Lagrangian formulation in the context of primal-dual methods [16, 18] or sequential quadratic programming methods [1... |

75 | Primal-dual interior methods for nonconvex nonlinear programming - FORSGREN, GILL - 1998 |

52 | Augmented lagrangian methods under the constant positive linear dependence constraint qualification
- Andreani, Birgin, et al.
(Show Context)
Citation Context ...ropriate updating strategy of the parameters σ and λ. Augmented Lagrangian methods have been fully studied in the past, see, e.g., [5, 10]. Some efficient software like LANCELOT-A [8, 9] and ALGENCAN =-=[1, 2, 6]-=- have been developed. There is a recent revival of algorithms based on an augmented Lagrangian formulation in the context of primal-dual methods [16, 18] or sequential quadratic programming methods [1... |

47 |
MA57—a code for the solution of sparse symmetric definite and indefinite systems.
- DUFF
- 2004
(Show Context)
Citation Context ...is a regularization parameter chosen to get a matrix of correct inertia. The choice of the regularization parameter δ is described in [4]. The factorization of Jk is done by means of the routine MA57 =-=[13]-=-. The stopping tolerance at Step 5 is defined by the formula εk = 0.9 max{‖Φ(wi, λi, σi)‖∞ : (k − 4)+ ≤ i ≤ k}+ 10σk, This choice has been successfully used in [4]. The convergence of the sequence {εk... |

22 | An algorithm for degenerate nonlinear programming with rapid local convergence. - Wright - 2005 |

21 | A primal-dual trust region algorithm for nonlinear optimization.
- Gill
- 2004
(Show Context)
Citation Context ...]. Note that, in the context of primal-dual algorithms, this regularization property is not specific to an augmented Lagrangian method, but also can be derived by introducing a quadratic penalty, see =-=[4, 7, 17, 26]-=-. In these algorithms, the linear system to solve at each iteration looks like the above linear system but without the parameter λ. This means that the equality constraints c = 0 are perturbed and so ... |

16 | Practical Augmented Lagrangian Methods for Constrained Optimization
- Birgin, Mart́ınez
- 2014
(Show Context)
Citation Context ...ropriate updating strategy of the parameters σ and λ. Augmented Lagrangian methods have been fully studied in the past, see, e.g., [5, 10]. Some efficient software like LANCELOT-A [8, 9] and ALGENCAN =-=[1, 2, 6]-=- have been developed. There is a recent revival of algorithms based on an augmented Lagrangian formulation in the context of primal-dual methods [16, 18] or sequential quadratic programming methods [1... |

16 | Local convergence of exact and inexact augmented Lagrangian methods under the second-order sufficient optimality condition.
- Fernández, Solodov
- 2012
(Show Context)
Citation Context ...ial quadratic programming methods [19]. An interesting feature of an augmented Lagrangian method is its regularization property and this leads to the formulation of stabilized SQP methods, see, e.g., =-=[14]-=- and the numerous references given within [19]. Note that, in the context of primal-dual algorithms, this regularization property is not specific to an augmented Lagrangian method, but also can be der... |

16 | A primal–dual augmented Lagrangian
- Gill, Robinson
(Show Context)
Citation Context ... software like LANCELOT-A [8, 9] and ALGENCAN [1, 2, 6] have been developed. There is a recent revival of algorithms based on an augmented Lagrangian formulation in the context of primal-dual methods =-=[16, 18]-=- or sequential quadratic programming methods [19]. An interesting feature of an augmented Lagrangian method is its regularization property and this leads to the formulation of stabilized SQP methods, ... |

14 |
An interior point method with a primal-dual quadratic barrier penalty function for nonlinear optimization
- Yamashita, Yabe
(Show Context)
Citation Context ...]. Note that, in the context of primal-dual algorithms, this regularization property is not specific to an augmented Lagrangian method, but also can be derived by introducing a quadratic penalty, see =-=[4, 7, 17, 26]-=-. In these algorithms, the linear system to solve at each iteration looks like the above linear system but without the parameter λ. This means that the equality constraints c = 0 are perturbed and so ... |

9 | Interior-point l(2)-penalty methods for nonlinear programming with strong global convergence properties
- Chen, Goldfarb
- 2006
(Show Context)
Citation Context ...]. Note that, in the context of primal-dual algorithms, this regularization property is not specific to an augmented Lagrangian method, but also can be derived by introducing a quadratic penalty, see =-=[4, 7, 17, 26]-=-. In these algorithms, the linear system to solve at each iteration looks like the above linear system but without the parameter λ. This means that the equality constraints c = 0 are perturbed and so ... |

9 | A globally convergent stabilized SQP method
- Gill, Robinson
- 1983
(Show Context)
Citation Context ...6] have been developed. There is a recent revival of algorithms based on an augmented Lagrangian formulation in the context of primal-dual methods [16, 18] or sequential quadratic programming methods =-=[19]-=-. An interesting feature of an augmented Lagrangian method is its regularization property and this leads to the formulation of stabilized SQP methods, see, e.g., [14] and the numerous references given... |

8 |
A primal-dual regularized interior-point method for convex quadratic programming
- Friedlander, Orban
- 2010
(Show Context)
Citation Context ... software like LANCELOT-A [8, 9] and ALGENCAN [1, 2, 6] have been developed. There is a recent revival of algorithms based on an augmented Lagrangian formulation in the context of primal-dual methods =-=[16, 18]-=- or sequential quadratic programming methods [19]. An interesting feature of an augmented Lagrangian method is its regularization property and this leads to the formulation of stabilized SQP methods, ... |

7 |
Primal-Dual Methods for Nonlinear Optimization.
- Robinson
- 2007
(Show Context)
Citation Context ... allowed to increase by means of a procedure of [4], and on the scaling parameter ν > 0 whose value is determined at the beginning of the inner iterations. This merit function, introduced by Robinson =-=[22]-=- and Gill and Robinson [18], is called generalized primaldual augmented Lagrangian. It is easy to see that w is a stationary point of ϕλ,σ,ν if and only if Φ(w, λ, σ) = 0. An interesting property, pro... |

4 |
From global to local convergence of interior methods for nonlinear optimization
- Armand, Benoist, et al.
(Show Context)
Citation Context ... The global and asymptotic convergence analysis of the outer iterations are much trickier because of the existence of the barrier trajectory, but could be carried out following the tools developed in =-=[3]-=-. A superlinear rate of convergence is expected. We plan to do it in a near future. 19 Acknowledgements The authors would like to thank the referees for valuable comments and suggestions which helped ... |

4 |
Robustness, generality and efficiency of optimization algorithms for practical applications, Struct
- Thanedar, Arora, et al.
- 1990
(Show Context)
Citation Context ...oblem if it succeeds in finding an optimal solution and we say that it is efficient if it requires fewer function evaluations (gradient evaluations, iterations, . . . ) for this computation, see e.g. =-=[23]-=-. Efficiency and robustness rates are readable on the left and right vertical axes of a graph. From Figure 1, SPDOPT-AL appears to be more efficient than both versions of SPDOPT-QP. In fact, for stand... |

3 |
On the local quadratic convergence of the primal–dual augmented Lagrangian method
- Polyak
(Show Context)
Citation Context ...can be proved on condition that the penalty parameter satisfies σ = Θ(‖(g + Ay, c)‖). Note that the local quadratic convergence of a primal-dual augmented Lagrangian method has been already proved in =-=[21]-=-, but the analysis is carried out without a globalization strategy as we propose in the present paper. To compare with a traditional augmented Lagrangian algorithm, like ALGENCAN or LANCELOT-A, and al... |

2 |
Study of a primal-dual method for equality constrained minimization
- Armand, Benoist, et al.
- 2014
(Show Context)
Citation Context |