Skip to main content
SpringerLink
Log in

Numerical comparison of merit function with filter criterion in inexact restoration algorithms using hard-spheres problems

  • Published:
Computational Optimization and Applications Aims and scope Submit manuscript

Abstract

Inexact Restoration methods have been introduced for solving nonlinear programming problems. Each iteration is composed of two phases. The first one reduces a measure of infeasibility, while in the second one the objective function value is reduced in a tangential approximation of the feasible set. The point obtained from the second phase is compared with the current point either by means of a merit function or by using a filter criterion. A comparative numerical study about these criteria by using a family of Hard-Spheres Problems is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abadie, J., Carpentier, J.: Generalization of the Wolfe reduced-gradient method to the case of nonlinear constraints. In: Fletcher, R. (ed.) Optimization, pp. 37–47. Academic Press, New York (1968)

    Google Scholar 

  2. Byrd, R.H.: Robust Trust Region Methods for Constrained Optimization, Third SIAM Conference on Optimization, Houston, TX, 1987

  3. Celis, M.R., Dennis, J.E., Tapia, R.A.: A trust region strategy for nonlinear equality constrained optimization. In: Boggs, P.T., Byrd, R.H. (eds.) Numerical Optimization 1984, pp. 71–82. SIAM, Philadelphia (1985)

    Google Scholar 

  4. Chin, C.M.: A new trust region based SLP-filter algorithm which uses EQP active set strategy. Ph.D. thesis, Department of Mathematics, University of Dundee, Scotland (2001)

  5. Conn, A.R., Gould, N.I.M., Toint, P.L.: Global convergence of a class of trust region algorithms for optimization with simple bounds. SIAM J. Numer. Anal. 25, 433–460 (1988). See also SIAM J. Numer. Anal. 26, 764–767 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  6. Conn, A.R., Gould, N.I.M., Toint, P.L.: LANCELOT: a Fortran Package for Large Scale Nonlinear Optimization (Release A). Springer Series in Computational Mathematics, vol. 17, Springer, New York (1992)

    MATH  Google Scholar 

  7. Conway, J.H., Sloane, N.J.C.: Sphere Packings, Lattices and Groups. Springer, New York (1988)

    MATH  Google Scholar 

  8. Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201–213 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  9. Fletcher, R., Gould, N., Leyffer, S., Toint, P., Wächter, A.: Global convergence of trust-region and SQP-filter algorithms for general nonlinear programming. SIAM J. Optim. 13(3), 635–659 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fletcher, R., Leyffer, S.: Nonlinear programming without a penalty function. Math. Program. Ser. A 91(2), 239–269 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. Gomes, F.A.M., Maciel, M.C., Martínez, J.M.: Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters. Math. Program. 84(1), 161–200 (1999)

    MATH  MathSciNet  Google Scholar 

  12. Gonzaga, C.C., Karas, E.W., Vanti, M.: A globally convergent filter method for nonlinear programming. SIAM J. Optim. 14(3), 646–669 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  13. Karas, E.W., Oening, A.P., Ribeiro, A.A.: Global convergence of slanting filter methods for nonlinear programming. Appl. Math. Comput. (2008). doi:10.1016/j.amc.2007.11.043

    MathSciNet  Google Scholar 

  14. Krejić, N., Martínez, J.M., Mello, M., Pilotta, E.A.: Validation of an augmented Lagrangian algorithm with a Gauss-Newton Hessian approximation using a set of hard-spheres problems. Comput. Optim. Appl. 16, 247–263 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  15. Martínez, J.M.: Inexact-Restoration method with Lagrangian tangent decrease and a new merit function for nonlinear programming. J. Optim. Theory Appl. 111, 39–58 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  16. Martínez, J.M., Pilotta, E.A.: Inexact Restoration algorithm for constrained optimization. J. Optim. Theory Appl. 104, 135–163 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  17. Martínez, J.M., Pilotta, E.A.: Inexact Restoration methods for nonlinear programming: Advances and perspectives. In: Qi, Teo, Yang (eds.) Optimization and Control with Applications, pp. 271–292. Springer, Berlin (2005)

    Chapter  Google Scholar 

  18. Murtagh, R.B., Saunders, M.A.: Minos 5.4 user’s guide. Technical report SOL-83-20, Stanford University (1995)

  19. Musin, O.R.: The kissing number in four dimensions. Technical report, Institute for Mathematical Study of Complex Systems, Moscow State University, Russia (April 2005)

  20. Omojokun, E.: Trust region algorithms for optimization with nonlinear equality and inequality constraints. Ph.D. thesis, Dept. of Computer Science, University of Colorado (1991)

  21. Rosen, J.B.: The gradient projection method for nonlinear programming, part 1: linear constraints. SIAM J. Appl. Math. 8, 181–217 (1960)

    Article  MATH  Google Scholar 

  22. Saaf, E.B., Kuijlaars, A.B.: Distributing many points on a sphere. Math. Intel. 19, 5 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Paraná, C.P. 19081, 81531-980, Curitiba, PR, Brasil

    Elizabeth W. Karas & Ademir A. Ribeiro

  2. Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, CIEM (CONICET), Medina Allende s/n, Ciudad Universitaria, 5000, Córdoba, Argentina

    Elvio A. Pilotta

Authors
  1. Elizabeth W. Karas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Elvio A. Pilotta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ademir A. Ribeiro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Elvio A. Pilotta.

Electronic Supplementary Material

Rights and permissions

Reprints and permissions

About this article

Cite this article

Karas, E.W., Pilotta, E.A. & Ribeiro, A.A. Numerical comparison of merit function with filter criterion in inexact restoration algorithms using hard-spheres problems. Comput Optim Appl 44, 427–441 (2009). https://doi.org/10.1007/s10589-007-9162-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10589-007-9162-5

Keywords

Search

Navigation