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A modified nonmonotone hestenes-Stiefel type conjugate gradient methods for large-scale unconstrained problems. (English) Zbl 1362.90341

Summary: 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.

MSC:

90C30 Nonlinear programming
90C06 Large-scale problems in mathematical programming
90C52 Methods of reduced gradient type
90C53 Methods of quasi-Newton type
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