How much do approximate derivatives hurt filter methods?

Caroline Sainvitu

RAIRO - Operations Research (2009)

  • Volume: 43, Issue: 3, page 309-329
  • ISSN: 0399-0559

Abstract

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In this paper, we examine the influence of approximate first and/or second derivatives on the filter-trust-region algorithm designed for solving unconstrained nonlinear optimization problems and proposed by Gould, Sainvitu and Toint in [12]. Numerical experiments carried out on small-scaled unconstrained problems from the CUTEr collection describe the effect of the use of approximate derivatives on the robustness and the efficiency of the filter-trust-region method.

How to cite

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Sainvitu, Caroline. "How much do approximate derivatives hurt filter methods?." RAIRO - Operations Research 43.3 (2009): 309-329. <http://eudml.org/doc/250621>.

@article{Sainvitu2009,
abstract = { In this paper, we examine the influence of approximate first and/or second derivatives on the filter-trust-region algorithm designed for solving unconstrained nonlinear optimization problems and proposed by Gould, Sainvitu and Toint in [12]. Numerical experiments carried out on small-scaled unconstrained problems from the CUTEr collection describe the effect of the use of approximate derivatives on the robustness and the efficiency of the filter-trust-region method. },
author = {Sainvitu, Caroline},
journal = {RAIRO - Operations Research},
keywords = {Unconstrained optimization; filter techniques; trust-region algorithms; approximate derivatives; numerical results.; unconstrained optimization; trust-region algorithms; numerical results},
language = {eng},
month = {7},
number = {3},
pages = {309-329},
publisher = {EDP Sciences},
title = {How much do approximate derivatives hurt filter methods?},
url = {http://eudml.org/doc/250621},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Sainvitu, Caroline
TI - How much do approximate derivatives hurt filter methods?
JO - RAIRO - Operations Research
DA - 2009/7//
PB - EDP Sciences
VL - 43
IS - 3
SP - 309
EP - 329
AB - In this paper, we examine the influence of approximate first and/or second derivatives on the filter-trust-region algorithm designed for solving unconstrained nonlinear optimization problems and proposed by Gould, Sainvitu and Toint in [12]. Numerical experiments carried out on small-scaled unconstrained problems from the CUTEr collection describe the effect of the use of approximate derivatives on the robustness and the efficiency of the filter-trust-region method.
LA - eng
KW - Unconstrained optimization; filter techniques; trust-region algorithms; approximate derivatives; numerical results.; unconstrained optimization; trust-region algorithms; numerical results
UR - http://eudml.org/doc/250621
ER -

References

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  1. R.H. Byrd, P. Lu, J. Nocedal and C. Zhu, A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput.16 (1995) 1190–1208.  Zbl0836.65080
  2. A.R. Conn, N.I.M. Gould and P.L. Toint, Convergence of quasi-Newton matrices generated by the Symmetric Rank One update. Math. Program.50 (1991) 177–196.  Zbl0737.90062
  3. A.R. Conn, N.I.M. Gould and P.L. Toint, Trust-Region Methods. MPS-SIAM Series on Optimization 1, SIAM, Philadelphia, USA (2000).  Zbl0958.65071
  4. A.R. Conn, K. Scheinberg and P.L. Toint, Recent progress in unconstrained nonlinear optimization without derivatives. Math. Program. Ser. B79 (1997) 397–414.  Zbl0887.90154
  5. E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles. Math. Program.91 (2002) 201–213.  Zbl1049.90004
  6. R. Fletcher and S. Leyffer, Nonlinear programming without a penalty function. Math. Program.91 (2002) 239–269.  Zbl1049.90088
  7. N.I.M. Gould, S. Leyffer and P.L. Toint, A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares. SIAM J. Optim.15 (2005) 17–38.  Zbl1075.65075
  8. N.I.M. Gould, S. Lucidi, M. Roma and P.L. Toint, Solving the trust-region subproblem using the Lanczos method. SIAM J. Optim.9 (1999) 504–525.  Zbl1047.90510
  9. N.I.M. Gould, D. Orban, A. Sartenaer and P.L. Toint, Sensitivity of trust-region algorithms on their parameters. 4OR, Quarterly Journal of Operations Research 3 (2005) 227–241.  Zbl1086.65060
  10. N.I.M. Gould, D. Orban and P.L. Toint, CUTEr, a constrained and unconstrained testing environment, revisited ACM Trans. Math. Software29 (2003) 373–394.  Zbl1068.90526
  11. N.I.M. Gould, D. Orban and P.L. Toint, GALAHAD — a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. ACM Trans. Math. Software29 (2003) 353–372.  Zbl1068.90525
  12. N.I.M. Gould, C. Sainvitu and P.L. Toint, A Filter-Trust-Region Method for Unconstrained Optimization. SIAM J. Optim.16 (2005) 341–357.  Zbl1122.90074
  13. N.I.M. Gould and P.L. Toint, FILTRANE, a Fortran 95 Filter-Trust-Region Package for Solving Systems of Nonlinear Equalities, Nonlinear Inequalities and Nonlinear Least-Squares Problems. Technical report 03/15, Rutherford Appleton Laboratory, Chilton, Oxfordshire, UK (2003).  
  14. D.C. Liu and J. Nocedal, On the limited memory BFGS method for large scale optimization. Math. Program. Ser. B45 (1989) 503–528.  Zbl0696.90048
  15. D.F. Shanno and K.H. Phua, Matrix conditionning and nonlinear optimization. Math. Program.14 (1978) 149–160.  Zbl0371.90109

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