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A modified conjugate gradient algorithm with cyclic Barzilai-Borwein steplength for unconstrained optimization. (English) Zbl 1253.65101

From the authors’ abstract: For solving large-scale unconstrained minimization problems, the nonlinear conjugate gradient method is welcome due to its simplicity, low storage, efficiency and nice convergence properties. Among all the methods in the framework, the conjugate gradient descent algorithm – CG_DESCENT is very popular, in which the generated directions descend automatically, and this nice property is independent of any line search used.

In this paper, the authors generalize CG_DESCENT with two Barzilai-Borwein steplength reused cyclically. It is shown that the resulting algorithm owns an attractive sufficient descent property and converges globally under some mild conditions. The proposed algorithm is tested by using a large set of unconstrained problems with high dimensions in CUTEr library. The numerical comparisons with the state-of-the-art algorithm CG_DESCENT illustrate that the proposed method is effective, competitive, and promising.

##### MSC:
 65K05 Mathematical programming (numerical methods) 90C06 Large-scale problems (mathematical programming) 90C30 Nonlinear programming
##### Software:
CUTEr; CG_DESCENT