Operations Research Transactions ›› 2012, Vol. 16 ›› Issue (3): 100-108.

• Original Articles • Previous Articles     Next Articles

The convergence of Broyden algorithms without convexity and exact line search

PU Dingguo1,2, SHANG Youlin1, FANG Aifen1, SUN Zhenyang1   

  1. 1. Department of Mathematics, Henan University of Science and Technology 2. Department of Mathematics, Tongji University
  • Received:2011-06-01 Revised:2012-02-28 Online:2012-09-15 Published:2012-09-18
  • Contact: Pu Dingguo E-mail:madpu@tongji.edu.cn
  • Supported by:

    National Science Foundation of China (Nos. 10771162, U1135003)

Abstract: In this paper we discuss the convergence of the  Broyden algorithms without convexity and exact line search assumptions. We prove that if  the algorithm produces a convergence point sequence, then the limit point of the sequence is  a critical point of the objective function.

Key words: Broyden algorithms, convergence, convexity, exact line search

CLC Number: