GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization

Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L.

doi:10.1145/962437.962438

Cited by 151 publications

(126 citation statements)

References 23 publications

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“…We acknowledge WOUDC (http://woudc.org) for providing ozonesonde data sets. We acknowledge the GALA-HAD Fortran library used for V3.0 retrieval (Gould et al, 2003). J. Jia acknowledges funding by CSC (China Scholarship Council).…”

mentioning

confidence: 99%

Global validation of SCIAMACHY limb ozone data (versions 2.9 and 3.0, IUP Bremen) using ozonesonde measurements

Jia¹,

Rozanov²,

Ladstätter-Weißenmayer³

et al. 2015

Atmos. Meas. Tech.

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Abstract. In this paper, the latest SCIAMACHY limb ozone scientific vertical profiles, namely the current V2.9 and the upcoming V3.0, are extensively compared with ozonesonde data from the World Ozone and Ultraviolet Radiation Data Centre (WOUDC) database. The comparisons are made on a global scale from 2003 to 2011, involving 61 sonde stations. The retrieval processors used to generate V2.9 and V3.0 data sets are briefly introduced. The comparisons are discussed in terms of vertical profiles and stratospheric partial columns. Our results indicate that the V2.9 ozone profile data between 20 and 30 km are in good agreement with ground-based measurements, with less than 5 % relative differences in the latitude range of 90 • S-40 • N (with the exception of the tropical Pacific region, where an overestimation of more than 10 % is observed), which corresponds to less than 5 DU partial-column differences. In the tropics the differences are within 3 %. However, this data set shows a significant underestimation northwards of 40 • N (up to ∼ 15 %). The newly developed V3.0 data set reduces this bias to below 10 % while maintaining a good agreement southwards of 40 • N with slightly increased relative differences of up to 5 % in the tropics.

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mentioning

confidence: 99%

Global validation of SCIAMACHY limb ozone data (versions 2.9 and 3.0, IUP Bremen) using ozonesonde measurements

Jia¹,

Rozanov²,

Ladstätter-Weißenmayer³

et al. 2015

Atmos. Meas. Tech.

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“…Algorithm dual-SCP implements dual subproblems (17), the dual subproblems are solved using the limited memory bound constrained L-BFGS-B solver (Zhu et al 1994). Algorithm QP-SCP implements QP subproblem (20), this time we use the diagonal Galahad LSQP solver (Gould et al 2004) to solve the QP subproblems. In the case of an infeasible subproblem the solver finds a subproblem solution with minimum constraint violation while respecting the imposed move limits.…”

Section: Numerical Examplementioning

confidence: 99%

First-order sequential convex programming using approximate diagonal QP subproblems

Etman

Groenwold

Rooda

2011

Struct Multidisc Optim

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Optimization algorithms based on convex separable approximations for optimal structural design often use reciprocal-like approximations in a dual setting; CONLIN and the method of moving asymptotes (MMA) are wellknown examples of such sequential convex programming (SCP) algorithms. We have previously demonstrated that replacement of these nonlinear (reciprocal) approximations by their own second order Taylor series expansion provides a powerful new algorithmic option within the SCP class of algorithms. This note shows that the quadratic treatment of the original nonlinear approximations also enables the restatement of the SCP as a series of Lagrange-Newton QP subproblems. This results in a diagonal trust-region SQP type of algorithm, in which the second order diagonal terms are estimated from the nonlinear (reciprocal) intervening variables, rather than from historic information using an exact or a quasi-Newton Hessian approach. The QP formulation seems particularly attractive for problems with far more constraints than variables (when pure dual methods are at a disadvantage), or when both the number of design variables and the number of (active) constraints is very large.

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“…In words, (14) states that when we predict a good reduction for the optimality part of the merit function, the step is only accepted if there exists a penalty parameter θ sup k ∈ [γ m , 1] such that A red /P red ≥ γ g . This condition seems to be somewhat inelegant, since one should expect that all of the iterates that do not belong to the forbidden region shown in Figure 2 are to be accepted.…”

Section: Mixing Merit Function and Filter Ideasmentioning

confidence: 99%

“…The selected problems are presented in Tables 1, 2 The algorithm, hereafter called GMM99, was implemented in FORTRAN 77 and the executable program was generated using the ifort 8.1 compiler, under the Fedora 3 Linux operating system. To evaluate its performance, the algorithm was compared to Lancelot (release B), the well known nonlinear programming package distributed along with the Galahad library [14]. The tests were performed on a Dell Optiplex GX280 computer, using an Intel Pentium 4, 540 processor, with a clock speed of 3.2GHz, 1MB of cache memory, a 800MHz front side bus and the Intel 915G chipset.…”

Section: Algorithm Performancementioning

confidence: 99%

A sequential quadratic programming algorithm that combines merit function and filter ideas

Gomes¹

2007

Mat. apl. comput.

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Abstract.A sequential quadratic programming algorithm for solving nonlinear programming problems is presented. The new feature of the algorithm is related to the definition of the merit function. Instead of using one penalty parameter per iteration and increasing it as the algorithm progresses, we suggest that a new point is to be accepted if it stays sufficiently below the piecewise linear function defined by some previous iterates on the ( f, C 2 2 )-space. Therefore, the penalty parameter is allowed to decrease between successive iterations. Besides, one need not to decide how to update the penalty parameter. This approach resembles the filter method introduced by Fletcher and Leyffer [Math. Program., 91 (2001), pp. 239-269], but it is less tolerant since a merit function is still used. Numerical comparison with standard methods shows that this strategy is promising. 65K05, 90C55, 90C30, 90C26. Mathematical subject classification:

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GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization

Cited by 151 publications

References 23 publications

Global validation of SCIAMACHY limb ozone data (versions 2.9 and 3.0, IUP Bremen) using ozonesonde measurements

Global validation of SCIAMACHY limb ozone data (versions 2.9 and 3.0, IUP Bremen) using ozonesonde measurements

First-order sequential convex programming using approximate diagonal QP subproblems

A sequential quadratic programming algorithm that combines merit function and filter ideas

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