, 56:2 | Cite as

A new class of conjugate gradient methods for unconstrained smooth optimization and absolute value equations

  • Farzad Rahpeymaii
  • Keyvan AminiEmail author
  • Tofigh Allahviranloo
  • Mohsen Rostamy Malkhalifeh


In this paper, we introduce a new three-term conjugate gradient (NTTCG) method to solve unconstrained smooth optimization problems. NTTCG is based on conjugate gradient methods proposed by Dai and Yuan (SIAM J Optim 10:177–182, 1999) and Polak and Ribière (Rev Francaise Inform Rech Oper 3(16):35–43, 1969). The descent property of the direction generated by NTTCG in each iteration is established. Under some standard assumptions, the global convergence results of the new methods are investigated. The extension of this algorithm is proposed to solve absolute value equations (AVE), called three-term conjugate subgradient (NTTCS) method. Numerical experiments are reported for unconstrained CUTEst problems and AVE.


Conjugate gradient method Smooth optimization Conjugate subgradient method Absolute value equations Wolfe conditions 

Mathematics Subject Classification

90C30 93E24 34A34 



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Copyright information

© Istituto di Informatica e Telematica (IIT) 2018

Authors and Affiliations

  • Farzad Rahpeymaii
    • 1
  • Keyvan Amini
    • 2
    Email author
  • Tofigh Allahviranloo
    • 1
  • Mohsen Rostamy Malkhalifeh
    • 1
  1. 1.Department of Mathematics, Science and Research BranchIslamic Azad UniversityTehranIran
  2. 2.Department of Mathematics, Faculty of SciencesRazi UniversityKermanshahIran

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