Skip to main content
SpringerLink
Log in

MPRGP for Bound Constrained QP

  • Chapter
  • First Online:
Scalable Algorithms for Contact Problems

Part of the book series: Advances in Mechanics and Mathematics ((AMMA,volume 36))

  • 123 Accesses

Abstract

We shall be concerned with the solution to the so-called bound constrained problems that appear in the dual formulation of both static and dynamic contact problems without friction.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Dostál, Z.: Optimal Quadratic Programming Algorithms, with Applications to Variational Inequalities, 1st edn. Springer, New York (2009)

    MATH  Google Scholar 

  2. Friedlander, A., Martínez, J.M.: On the maximization of a concave quadratic function with box constraints. SIAM J. Optim. 4, 177–192 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dostál, Z.: Box constrained quadratic programming with proportioning and projections. SIAM J. Optim. 7(3), 871–887 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dostál, Z., Domorádová, M., Sadowská, M.: Superrelaxation in minimizing quadratic functions subject to bound constraints. Comput. Optim. Appl. 48(1), 23–44 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. van der Sluis, A., van der Vorst, H.A.: The rate of convergence of the conjugate gradients. Numer. Math. 48, 543–560 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  6. Moré, J.J., Toraldo, G.: On the solution of large quadratic programming problems with bound constraints. SIAM J. Optim. 1, 93–113 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  7. Dostál, Z., Schöberl, J.: Minimizing quadratic functions over non-negative cone with the rate of convergence and finite termination. Comput. Optim. Appl. 30(1), 23–44 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. O’Leary, D.P.: A generalised conjugate gradient algorithm for solving a class of quadratic programming problems. Linear Algebra Appl. 34, 371–399 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hestenes, M.R., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. 49, 409–436 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  10. Polyak, B.T.: The conjugate gradient method in extremal problems. USSR Comput. Math. Math. Phys. 9, 94–112 (1969)

    Article  MATH  Google Scholar 

  11. Calamai, P.H., Moré, J.J.: Projected gradient methods for linearly constrained problems. Math. Program. 39, 93–116 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  12. Nocedal, J., Wright, S.F.: Numerical Optimization. Springer, New York (2000)

    MATH  Google Scholar 

  13. Friedlander, A., Martínez, J.M., Raydan, M.: A new method for large scale box constrained quadratic minimization problems. Optim. Methods Softw. 5, 57–74 (1995)

    Article  Google Scholar 

  14. Bielschowski, R.H., Friedlander, A., Gomes, F.A.M., Martínez, J.M., Raydan, M.: An adaptive algorithm for bound constrained quadratic minimization. Invest. Oper. 7, 67–102 (1997)

    Google Scholar 

  15. Diniz-Ehrhardt, M.A., Gomes-Ruggiero, M.A., Santos, S.A.: Numerical analysis of the leaving-face criterion in bound-constrained quadratic minimization. Optim. Methods Softw. 15(1), 45–66 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  16. Schöberl, J.: Solving the Signorini problem on the basis of domain decomposition techniques. Computing 60(4), 323–344 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  17. Schöberl, J.: Efficient contact solvers based on domain decomposition techniques. Comput. Math. Appl. 42, 1217–1228 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Dostál, Z.: On the decrease of a quadratic function along the projected-gradient path. ETNA 31, 25–59 (2008)

    MathSciNet  MATH  Google Scholar 

  19. Dostál, Z.: A proportioning based algorithm for bound constrained quadratic programming with the rate of convergence. Numer. Algorithms 34(2–4), 293–302 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  20. Dostál, Z., Kozubek, T., Brzobohatý, T., Markopoulos, A., Vlach, O.: Scalable TFETI with optional preconditioning by conjugate projector for transient contact problems of elasticity. Comput. Methods Appl. Mech. Eng. 247–248, 37–50 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. di Serafino, D., Ruggiero, V., Toraldo, G., Zanni, L.: On the steplength selection in gradient methods for unconstrained optimization. Appl. Math. Comput. 318, 176–195(2017)

    Article  MathSciNet  MATH  Google Scholar 

  22. Dostál, Z., Toraldo, G., Viola, M., Vlach, O.: Proportionality-Based Gradient Methods with Applications in Contact Mechanics. In: Kozubek, T. et al. (eds.) Procceedings of HPCSE 2017—High Performance Computing in Science and Engineering. LNCSE, vol. 11087, pp. 47–58. Springer, Cham (2018)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics and IT4Innovations National Supercomputing Center, VŠB-Technical University of Ostrava, Ostrava, Czech Republic

    Zdeněk Dostál

Authors
  1. Zdeněk Dostál
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zdeněk Dostál .

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Dostál, Z. (2023). MPRGP for Bound Constrained QP. In: Scalable Algorithms for Contact Problems. Advances in Mechanics and Mathematics, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-031-33580-8_8

Download citation

Publish with us

Policies and ethics

Search

Navigation