A new class of quasi-Newton updating formulas

Donghui Li, Liqun Qi, Vera Roshchina

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)


In this paper, we propose a derivative-free quasi-Newton condition, which results in a new class of quasi-Newton updating formulas for unconstrained optimization. Each updating formula in this class is a rank-two updating formula and preserves the positive definiteness of the second derivative matrix of the quadratic model. Its first two terms are the same as the first two terms of the BFGS updating formula. We establish global convergence of quasi-Newton methods based upon the updating formulas in this class, and superlinear convergence of a special quasi-Newton method among them. Then we propose a special quasi-Newton updating formula, which repetitively uses the new quasi-Newton condition. This updating formula is derivative-free. Numerical results are reported.
Original languageEnglish
Pages (from-to)237-249
Number of pages13
JournalOptimization Methods and Software
Issue number2
Publication statusPublished - 1 Apr 2008


  • Convergence
  • Derivative-free conditions
  • Positive definiteness
  • Rank-two quasi-Newton updating formulas
  • Unconstrained optimization

ASJC Scopus subject areas

  • Software
  • Control and Optimization
  • Applied Mathematics


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