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...

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...

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...

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...

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...

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...

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...

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 ...

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...

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...

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, ...

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 ...

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 ...

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...

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, ...

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...

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 ...

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...

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...

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 ...