Skip to main content

Performance Profiles of Conjugate-Gradient Algorithms for Unconstrained Optimization

  • Reference work entry
Book cover Encyclopedia of Optimization

Article Outline

Keywords and Phrases

Introduction

Classical Conjugate-Gradient Algorithms

Hybrid Conjugate-Gradient Methods

Scaled Conjugate-Gradient Algorithms

SCALCG Algorithm

Modified Conjugate-Gradient Algorithms

Parametric Conjugate-Gradient Algorithms

Performance Profiles

Conclusion and Discussion

References

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 2,500.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 2,499.99
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. Andrei N (2007) Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization. Optim Methods Softw 22:561–571

    Article  MathSciNet  MATH  Google Scholar 

  2. Andrei N (2007) A scaled BFGS preconditioned conjugate gradient algorithm for unconstrained optimization. Appl Math Lett 20:645–650

    Article  MathSciNet  MATH  Google Scholar 

  3. Andrei N, Scaled conjugate gradient algorithms for unconstrained optimization. Comput Optim Appl 38:401–416

    Google Scholar 

  4. Andrei N (2007) A scaled nonlinear conjugate gradient algorithm for unconstrained optimization. http://www.informaworld.com/smpp/content%7Econtent= a779773265%7Edb=all%7Eorder=pubdate: First published on: 21 June 2007

  5. Andrei N (2008) A Dai-Yuan conjugate gradient algorithm with sufficient descent and conjugacy conditions for unconstrained optimization. Appl Math Lett 21:165–171

    Article  MATH  MathSciNet  Google Scholar 

  6. Andrei N, Test functions for unconstrained optimization. http://www.ici.ro/camo/neculai/SCALCG/evalfg.for

  7. Andrei N (2007) New hybrid conjugate gradient algorithms for unconstrained optimization. ICI Thechnical Report, September 26

    Google Scholar 

  8. Andrei N (2007) Another hybrid conjugate gradient algorithm for unconstrained optimization. ICI Technical Report, July 18

    Google Scholar 

  9. Andrei N (2007) Another nonlinear conjugate gradient algorithm for unconstrained optimization. ICI Thechnical Report, May 16

    Google Scholar 

  10. Birgin E, Martínez M (2001) A spectral conjugate gradient method for unconstrained optimization. Appl Math Optim 43:117–128

    Article  MathSciNet  MATH  Google Scholar 

  11. Bongartz I, Conn AR, Gould NIM, Toint PL (1995) CUTE: constrained and unconstrained testing environments. ACM Trans Math Softw 21:123–160

    Article  MATH  Google Scholar 

  12. Dai YH, Liao LZ (2001), New conjugacy conditions and related nonlinear conjugate gradient methods. Appl Math Optim 43:87–101

    Article  MathSciNet  MATH  Google Scholar 

  13. Dai YH, Yuan Y (1999) A nonlinear conjugate gradient method with a strong global convergence property. SIAM J Optim 10:177–182

    Article  MathSciNet  MATH  Google Scholar 

  14. Dai YH, Yuan Y (2001) A three-parameter family of hybrid conjugate gradient method. Math Comput 70:1155–1167

    MathSciNet  MATH  Google Scholar 

  15. Dai YH, Yuan Y (2003) A class of globally convergent conjugate gradient methods. Sci China Ser A 46:251–261

    Article  MathSciNet  Google Scholar 

  16. Dolan ED, Moré JJ (2002) Benchmarcking optimization software with performance profiles. Math Program 91:201–213

    Article  MathSciNet  MATH  Google Scholar 

  17. Fletcher R (1987) Practical Methods of Optimization, 2nd edn. Wiley, Chichester

    MATH  Google Scholar 

  18. Fletcher R, Reeves C (1964) Function minimization by conjugate gradients. Comput J 7:149–154

    Article  MathSciNet  MATH  Google Scholar 

  19. Gilbert JC, Nocedal J (1992) Global convergence properties of conjugate gradient methods. SIAM J Optim 2:21–42

    Article  MathSciNet  MATH  Google Scholar 

  20. Hager WW, Zhang H (2005) A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J Optim 16:170–192

    Article  MathSciNet  MATH  Google Scholar 

  21. Hager WW, Zhang H (2006) Algorithm 851: CG_DESCENT, A conjugate gradient method with guaranteed descent. ACM Trans Math Softw 32:113–137

    Article  MathSciNet  Google Scholar 

  22. Hager WW, Zhang H (2006), A survey of nonlinear conjugate gradient methods. Pac J Optim 2:35–58

    MATH  MathSciNet  Google Scholar 

  23. Hestenes MR, Stiefel E (1952) Methods of conjugate gradients for solving linear systems. J Res Nat Bur Stand Sec B 48:409–436

    MathSciNet  Google Scholar 

  24. Hu YF, Storey C (1991) Global convergence result for conjugate gradient methods. J Optim Theory Appl 71:399–405

    Article  MathSciNet  MATH  Google Scholar 

  25. Liu D, Nocedal J (1989) On the limited memory BFGS method for large scale optimization. Math Program B 45:503–528

    Article  MathSciNet  MATH  Google Scholar 

  26. Liu DC, Storey (1991) Efficient generalized conjugate gradient algorithms. Part 1: Theory. J Optim Theory Appl 69:129–137

    Article  MathSciNet  MATH  Google Scholar 

  27. Moré JJ, Thuente DJ (1994) Line search algorithms with guaranteed sufficient decrease. ACM Trans Math Softw 20:286–307

    Article  MATH  Google Scholar 

  28. Nazareth JL (1999) Conjugate gradient methods. In: Floudas C, Pardalos P (eds) Encyclopedia of Optimization. Kluwer, Boston

    Google Scholar 

  29. Nocedal J (1980) Updating quasi-Newton matrices with limited starage. Math Comput 35:773–782

    Article  MathSciNet  MATH  Google Scholar 

  30. Perry A (1978) A modified conjugate gradient algorithm. Oper Res 26:1073–1078

    MathSciNet  MATH  Google Scholar 

  31. Polak E, Ribière G (1969) Note sur la convergence de directions conjugées. Rev Francaise Informat Recherche Operationelle 3e Année 16:35–43

    Google Scholar 

  32. Polyak BT (1969) The conjugate gradient method in extreme problems. URSS Comp Math Math Phys 9:94–112

    Article  Google Scholar 

  33. Powell MJD (1984) Nonconvex minimization calculations and the conjugate gradient method. Numerical Analysis (Dundee, (1983)), Lecture Notes in Mathematics, vol 1066. Springer, Berlin, pp 122–141

    Google Scholar 

  34. Shanno DF (1978) Conjugate gradient methods with inexact searches. Math Oper Res 3:244–256

    MathSciNet  MATH  Google Scholar 

  35. Shanno DF (1978) On the convergence of a new conjugate gradient algorithm. SIAM J Numer Anal 15:1247–1257

    Article  MathSciNet  MATH  Google Scholar 

  36. Shanno DF, Phua KH (1976) Algorithm 500, Minimization of unconstrained multivariate functions. ACM Trans Math Softw 2:87–94

    Article  MATH  Google Scholar 

  37. Touati-Ahmed D, Storey C (1990) Efficient hybrid conjugate gradient techniques. J Optim Theory Appl 64:379–397

    Article  MathSciNet  MATH  Google Scholar 

  38. Yabe H, Takano M (2004) Global convergence properties of nonlinear conjugate gradient methods with modified secant conditions. Comput Optim Appl (COAP) 28:203–225

    Article  MathSciNet  MATH  Google Scholar 

  39. Zhang JZ, Deng NY, Chen LH (1999) New quasi-Newton equation and related methods for unconstrained optimization. J Optim Theory Appl 102:147–167

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Andrei, N. (2008). Performance Profiles of Conjugate-Gradient Algorithms for Unconstrained Optimization . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_506

Download citation

Publish with us

Policies and ethics