## Optimality measures for performance profiles (2004)

Venue: | Preprint ANL/MCS-P1155-0504, Mathematics and Computer Science Division, Argonne National Lab |

Citations: | 15 - 0 self |

### BibTeX

@INPROCEEDINGS{Dolan04optimalitymeasures,

author = {Elizabeth D. Dolan and Jorge J. Moré and Todd S. Munson and Elizabeth D. Dolan and Jorge J. Moré and Todd S. Munson},

title = {Optimality measures for performance profiles},

booktitle = {Preprint ANL/MCS-P1155-0504, Mathematics and Computer Science Division, Argonne National Lab},

year = {2004}

}

### OpenURL

### Abstract

We examine the influence of optimality measures on the benchmarking process, and show that scaling requirements lead to a convergence test for nonlinearly constrained solvers that uses a mixture of absolute and relative error measures. We show that this convergence test is well behaved at any point where the constraints satisfy the Mangasarian-Fromovitz constraint qualification and also avoids the explicit use of a complementarity measure. Our computational experiments explore the impact of this convergence test on the benchmarking process with performance profiles. 1

### Citations

246 | Benchmarking optimization software with performance profiles
- Dolan, Moré
(Show Context)
Citation Context ...so examine the scale invariance properties of other convergence tests. Sections 5 describes the benchmarking process based on the convergence test introduced in Section 3. We use performance profiles =-=[3]-=- and Version 3.0 of COPS [4], the Constrained Optimization Problem Set, to evaluate the effect of the convergence tests. Performance profiles have been used in a wide variety of benchmarking studies (... |

76 | J.J.: Newton’s method for large bound-constrained optimization problems - Lin, Moré - 1999 |

75 | User’s guide for SNOPT 5.3: A Fortran package for large-scale nonlinear programming
- Gill, Murray, et al.
- 1998
(Show Context)
Citation Context ... performed with the COPS 3.0 test set [4]. The following solvers were used for the experiments: KNITRO 3.0 [13], ASL (20020905) LOQO 6.02 [12], ASL (20020221) MINOS 5.5 [10], ASL (20020614) SNOPT 6.1 =-=[5]-=-, ASL (20020614) 13sAll of the computations were performed on an Intel Pentium 4 1.8 GHz CPU with 512 MB of RAM and a 256 KB cache, running Red Hat Linux 7.3. Furthermore, a time limit of 30 minutes w... |

50 |
MINOS 5.5 user’s guide
- Murtagh, Saunders
- 1983
(Show Context)
Citation Context ...rofiles for the two experiments performed with the COPS 3.0 test set [4]. The following solvers were used for the experiments: KNITRO 3.0 [13], ASL (20020905) LOQO 6.02 [12], ASL (20020221) MINOS 5.5 =-=[10]-=-, ASL (20020614) SNOPT 6.1 [5], ASL (20020614) 13sAll of the computations were performed on an Intel Pentium 4 1.8 GHz CPU with 512 MB of RAM and a 256 KB cache, running Red Hat Linux 7.3. Furthermore... |

29 | Numerical comparison of Augmented Lagrangian algorithms for nonconvex problems
- Birgin, Castillo, et al.
- 2005
(Show Context)
Citation Context ...3.0 of COPS [4], the Constrained Optimization Problem Set, to evaluate the effect of the convergence tests. Performance profiles have been used in a wide variety of benchmarking studies (for example, =-=[1, 2, 8, 9]-=-), but in almost all cases the convergence criteria have not been specified in detail. This is certainly the case for benchmarking studies in the AMPL or GAMS modeling environment because in these cas... |

15 |
Benchmarking optimization software with
- Dolan, Moré
(Show Context)
Citation Context ...nce properties of other convergence tests. Sections 5 describes the benchmarking process based on the convergence test introduced in Section 3. We use performance profiles [3] and Version 3.0 of COPS =-=[4]-=-, the Constrained Optimization Problem Set, to evaluate the effect of the convergence tests. Performance profiles have been used in a wide variety of benchmarking studies (for example, [1, 2, 8, 9]), ... |

7 |
An SQP algorithm for large-scale constrained optimization
- SNOPT
(Show Context)
Citation Context ...τc. (3.5) This is an important observation because (3.2) and (3.3) are closely related to convergence tests used by optimization solvers such as SNOPT and KNITRO. For example, instead of (3.2), SNOPT =-=[6]-=- requires that ck(x) ≤ τf , πk(x) ≤ τc, |ck(x)πk(x)| ≤ τc. (3.6) This is a stronger convergence test than (3.2) because if (3.6) holds, then |πk(x)| ≤ τc τf if |ck(x)| > τf . We also note that (3.6) n... |

6 |
KNITRO user’s manual – Version 3.1
- Waltz, Nocedal
- 2003
(Show Context)
Citation Context ...). |πk(x)| ≤ 1 σ Thus, for problems with large multipliers, this bound shows that τf may have to be relatively small in order to satisfy (3.6). Similar remarks apply to the optimization solver KNITRO =-=[13]-=-. The convergence test in KNITRO replaces (3.2) by τc τf . ck(x) ≤ τf , πk(x) < 0, |ck(x)πk(x)| ≤ τc. (3.7) Thus, the only difference between the convergence test in SNOPT and KNITRO is that KNITRO gu... |

5 | A comparative study of large-scale nonlinear optimization algorithms
- Benson, Shanno, et al.
- 2002
(Show Context)
Citation Context ...3.0 of COPS [4], the Constrained Optimization Problem Set, to evaluate the effect of the convergence tests. Performance profiles have been used in a wide variety of benchmarking studies (for example, =-=[1, 2, 8, 9]-=-), but in almost all cases the convergence criteria have not been specified in detail. This is certainly the case for benchmarking studies in the AMPL or GAMS modeling environment because in these cas... |

3 |
Assessing the potential of interior-point methods for nonlinear optimization
- Nocedal, Morales, et al.
(Show Context)
Citation Context ...3.0 of COPS [4], the Constrained Optimization Problem Set, to evaluate the effect of the convergence tests. Performance profiles have been used in a wide variety of benchmarking studies (for example, =-=[1, 2, 8, 9]-=-), but in almost all cases the convergence criteria have not been specified in detail. This is certainly the case for benchmarking studies in the AMPL or GAMS modeling environment because in these cas... |

2 |
Nonlinear optimization models. See www.sor.princeton.edu/~rvdb/ ampl/nlmodels
- Vanderbei
(Show Context)
Citation Context ... (including bounds). Our benchmarking results are done with a set of problems and solvers. We have used COPS, but we could have also used a selection of the engineering problems provided by Vanderbei =-=[11]-=-. Also note that timing data refers to a particular computing environment 1 12 1 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1sTable 5.1: Problem data (minimum, quartiles, maximum) for the COPS benchmark Prob... |

1 |
A server for automated performance analysis of benchmarking data, preprint, Performance World, 2003. Available at www.gamsworld.org/performance
- Mittlemann, Pruesner
(Show Context)
Citation Context |

1 |
user’s manual – Version 4.05
- LOQO
- 2000
(Show Context)
Citation Context ...gure 6.1 displays performance profiles for the two experiments performed with the COPS 3.0 test set [4]. The following solvers were used for the experiments: KNITRO 3.0 [13], ASL (20020905) LOQO 6.02 =-=[12]-=-, ASL (20020221) MINOS 5.5 [10], ASL (20020614) SNOPT 6.1 [5], ASL (20020614) 13sAll of the computations were performed on an Intel Pentium 4 1.8 GHz CPU with 512 MB of RAM and a 256 KB cache, running... |