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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.

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