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A numerical study of the limited memory BFGS method an the truncated- Newton method for large scale optimization. (English) Zbl 0756.65091
The authors consider the smooth unconstrained minimization problem: \(\min f(x)\), \(x\in\mathbb{R}^ n\). The limited memory Broyden-Fletcher-Goldfarb- Shanno (BFGS) method (L-BFGS) and the discrete truncated-Newton (TN) method are described; test problems and a numerical of the relative performance of L-BFGS and of TN-algorithms are presented. The authors prove that the conjugate gradient method is not competitive with TN or L- BFGS in terms of function evaluation. Detailed examples are given. The style is elegant.
Reviewer: P.Stavre (Craiova)

65K05 Numerical mathematical programming methods
90C06 Large-scale problems in mathematical programming
90C30 Nonlinear programming
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