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Broyden, C.G. (1970) The Convergence of a Class of Double-Rank Minimization Algorithms: I. General Considerations. Journal of the Institute of Mathematics and Its Applications, 6, 76-90.
https://doi.org/10.1093/imamat/6.1.76

has been cited by the following article:

• TITLE: A Scaled Conjugate Gradient Method Based on New BFGS Secant Equation with Modified Nonmonotone Line Search

  AUTHORS: Tsegay Giday Woldu, Haibin Zhang, Yemane Hailu Fissuh

  KEYWORDS: Conjugate Gradient Method, BFGS Method, Modified Secant Equation, Nonmonotone Line Search, Nonsmooth Optimization

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.10 No.1, January 8, 2020

  ABSTRACT: In this paper, we provide and analyze a new scaled conjugate gradient method and its performance, based on the modified secant equation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and on a new modified nonmonotone line search technique. The method incorporates the modified BFGS secant equation in an effort to include the second order information of the objective function. The new secant equation has both gradient and function value information, and its update formula inherits the positive definiteness of Hessian approximation for general convex function. In order to improve the likelihood of finding a global optimal solution, we introduce a new modified nonmonotone line search technique. It is shown that, for nonsmooth convex problems, the proposed algorithm is globally convergent. Numerical results show that this new scaled conjugate gradient algorithm is promising and efficient for solving not only convex but also some large scale nonsmooth nonconvex problems in the sense of the Dolan-Moré performance profiles.