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A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization. (English) Zbl 0886.65065
The following nonlinear programming problem with simple bounds on variables \[ \text{minimize }f(x)\quad\text{subject to }\ell\leq x\leq u \] is considered. The objective function \(f(x)\) is assumed to be twice continuously differentiable, \(\ell\) and \(u\) are given bound vectors in \(\mathbb{R}^n\), and \(n\) is the number of variables, which is assumed to be large.
The given subspace limited memory quasi-Newton algorithm does not need to solve any subproblems. The search direction of the algorithm consists of three parts: a subspace quasi-Newton direction, and two subspace gradient and modified gradient directions. The global convergence of the method is proved and some numerical results are given.

65K05 Numerical mathematical programming methods
90C06 Large-scale problems in mathematical programming
90C30 Nonlinear programming
Full Text: DOI
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