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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
##### Software:
CUTE; CUTEr; LANCELOT; L-BFGS; L-BFGS-B; LBFGS-B
Full Text:
##### References:
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