New nonlinear conjugate gradient formulas for large-scale unconstrained optimization problems

Zengxin Wei, Guoyin Li, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

67 Citations (Scopus)


We propose new conjugate gradient formulas for computing the search directions for unconstrained optimization problems. The new formulas turn out to be the conjugate descent formula if exact line searches are made. Some formulas possess the sufficient descent property without any line searches. General convergence results for the proposed formulas with the weak Wolfe-Powell conditions are studied. We prove that some of the formulas with the steplength technique which ensures the Zoutendijk condition to be held are globally convergent. In addition, the global convergence results for some other formulas with the standard Armijo line search are also given. Preliminary numerical results show that the proposed methods are very promising.
Original languageEnglish
Pages (from-to)407-430
Number of pages24
JournalApplied Mathematics and Computation
Issue number2
Publication statusPublished - 15 Aug 2006


  • Armijo line search
  • Global convergence
  • Large-scale
  • New conjugate gradient formulas
  • Unconstrained optimization
  • Wolfe-Powell conditions

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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