Open AccessA Conjugate Gradient Algorithm with Function Value Information and N-Step Quadratic Convergence for Unconstrained Optimization
Author(s) -
Xiangrong Li,
Xupei Zhao,
Xiabin Duan,
Xiaoliang Wang
Publication year - 2015
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0137166
Subject(s) - conjugate gradient method , convergence (economics) , quadratic equation , quadratic model , algorithm , function (biology) , mathematics , conjugate , value (mathematics) , mathematical optimization , computer science , mathematical analysis , statistics , biology , geometry , evolutionary biology , economics , economic growth , response surface methodology
It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence—with at most a linear convergence rate—because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP method in which the restart strategy is also used. Moreover, the method we developed includes not only n-step quadratic convergence but also both the function value information and gradient value information. In this paper, we will show that the new PRP method (with either the Armijo line search or the Wolfe line search) is both linearly and quadratically convergent. The numerical experiments demonstrate that the new PRP algorithm is competitive with the normal CG method.