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A compact limited memory method for large scale unconstrained optimization. (English) Zbl 1114.90072
Summary: A compact limited memory method for solving large scale unconstrained optimization problems is proposed. The compact representation of the quasi-Newton updating matrix is derived to the use in the form of limited memory update in which the vector \(y_{k}\) is replaced by a modified vector \(\hat y_k\) so that more available information about the function can be employed to increase the accuracy of Hessian approximations. The global convergence of the proposed method is proved. Numerical tests on commonly used large scale test problems indicate that the proposed compact limited memory method is competitive and efficient.

90C06 Large-scale problems in mathematical programming
90C52 Methods of reduced gradient type
90C30 Nonlinear programming
minpack; L-BFGS
Full Text: DOI
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