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GALAHAD, a library of threadsafe Fortran 90 Packages for LargeScale Nonlinear Optimization
, 2002
"... In this paper, we describe the design of version 1.0 of GALAHAD, a library of Fortran 90 packages for largescale largescale nonlinear optimization. The library particularly addresses quadratic programming problems, containing both interior point and active set variants, as well as tools for prepro ..."
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Cited by 19 (4 self)
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In this paper, we describe the design of version 1.0 of GALAHAD, a library of Fortran 90 packages for largescale largescale nonlinear optimization. The library particularly addresses quadratic programming problems, containing both interior point and active set variants, as well as tools for preprocessing such problems prior to solution. It also contains an updated version of the venerable nonlinear programming package, LANCELOT.
Constrained DerivativeFree Optimization on Thin Domains
, 2011
"... Many derivativefree methods for constrained problems are not efficient for minimizing functions on “thin” domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penaltylike strategies. When the constraints are computationally inexpensive but highly n ..."
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Cited by 1 (1 self)
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Many derivativefree methods for constrained problems are not efficient for minimizing functions on “thin” domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penaltylike strategies. When the constraints are computationally inexpensive but highly nonlinear, these methods spend many potentially expensive objective function evaluations motivated by the difficulties of improving feasibility. An algorithm that handles efficiently this case is proposed in this paper. The main iteration is splitted into two steps: restoration and minimization. In the restoration step the aim is to decrease infeasibility without evaluating the objective function. In the minimization step the objective function f is minimized on a relaxed feasible set. A global minimization result will be proved and computational experiments showing the advantages of this approach will be presented.
FULL LENGTH PAPER Nonlinear
"... programming without a penalty function or a filter ..."
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ERRATUM Erratum to: Nonlinear programming without a penalty function or a filter
, 2011
"... This note reports a correction to the results obtained by [2], in which an error was unfortunately discovered during work with D. Robinson. The problem is in the proof of Lemma 3.10 of this reference, where it is claimed that Lemma 6.5.3 of [1] can be invoked to deduce that ρck ≥ η2, where ρck is a ..."
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This note reports a correction to the results obtained by [2], in which an error was unfortunately discovered during work with D. Robinson. The problem is in the proof of Lemma 3.10 of this reference, where it is claimed that Lemma 6.5.3 of [1] can be invoked to deduce that ρck ≥ η2, where ρck is a specific ratio of achieved to predicted reduction is constraint violation and η2 is a constant in (0, 1). As it turns out, the reasoning is only correct if the ratio ‖sk‖/ ∥s Rk ∥ is bounded above, where sk is the step at iteration k and s Rk is its projection onto the range of the transposed Jacobian J Tk. Handling the case where this ratio is unbounded above turned out to be surprisingly complex. In particular, this required considering separately the cases where the tangential component of the step at iteration k is large or small with respect to its normal component, where the meaning of “large ” and “small ” has to be defined very specifically. The convergence proof taking this distinction into account is therefore significantly more involved than the proof of [2], and cannot be presented in the form of a few corrections in the original text. The report [4] (including substantial contribution by D. Robinson) proposes a corrected version of [2], where other minor The online version of the original article can be found under doi:10.1007/s1010700802447.