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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 $$\text{minimize }f(x)\quad\text{subject to }\ell\le x\le u$$ is considered. The objective function $f(x)$ is assumed to be twice continuously differentiable, $\ell$ and $u$ are given bound vectors in $\bbfR^n$, 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 Mathematical programming (numerical methods) 90C06 Large-scale problems (mathematical programming) 90C30 Nonlinear programming
##### Software:
CUTEr; LANCELOT; L-BFGS-B; L-BFGS
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