A Modified Nonmonotone Hestenes–Stiefel Type Conjugate Gradient Methods for Large-Scale Unconstrained Problems. (2nd January 2017) - Dong, Xiao-Liang; Liu, Hong-Wei; Li, Xiang-Li; He, Yu-Bo; Liu, Ze-Xian
ABSTRACT: In this article, by slightly modifying the search direction of the nonmonotone Hestenes–Stiefel method, a variant Hestenes–Stiefel conjugate gradient method is proposed that satisfies the suﬃcient descent condition independent of any line search. This algorithm also possesses information about the gradient value and the function value. We establish the global convergence of our methods without the assumption that the steplength is bounded away from zero. Numerical results illustrate that our method can eﬃciently solve the test problems, and therefore is promising.