New Hybrid Conjugate Gradient and Broyden–Fletcher–Goldfarb–Shanno Conjugate Gradient Methods

  • Predrag S. Stanimirović
  • Branislav Ivanov
  • Snežana Djordjević
  • Ivona Brajević


Three hybrid methods for solving unconstrained optimization problems are introduced. These methods are defined using proper combinations of the search directions and included parameters in conjugate gradient and quasi-Newton methods. The convergence of proposed methods with the underlying backtracking line search is analyzed for general objective functions and particularly for uniformly convex objective functions. Numerical experiments show the superiority of the proposed methods with respect to some existing methods in view of the Dolan and Moré’s performance profile.


Global convergence Backtracking line search Unconstrained optimization Conjugate gradient methods Quasi-Newton methods 

Mathematics Subject Classification




The first author gratefully acknowledge support from the Research Project 174013 of the Serbian Ministry of Science.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Predrag S. Stanimirović
    • 1
  • Branislav Ivanov
    • 2
  • Snežana Djordjević
    • 3
  • Ivona Brajević
    • 1
  1. 1.Faculty of Sciences and MathematicsUniversity of NišNisSerbia
  2. 2.Technical Faculty in BorUniversity of BelgradeBorSerbia
  3. 3.Faculty of Technology in LeskovacUniversity of NišLeskovacSerbia

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