A subspace limited memory quasi-Newton algorithm for large-scale nonlinear bound constrained optimization.

*(English)*Zbl 0886.65065The 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.

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.

Reviewer: H.Benker (Merseburg)

##### MSC:

65K05 | Numerical mathematical programming methods |

90C06 | Large-scale problems in mathematical programming |

90C30 | Nonlinear programming |

##### Keywords:

subspace quasi-Newton method; limited memory; projected search; large scale problem; bound constrained optimization; nonlinear programming; quasi-Newton algorithm; convergence; numerical results
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\textit{Q. Ni} and \textit{Y. Yuan}, Math. Comput. 66, No. 220, 1509--1520 (1997; Zbl 0886.65065)

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##### References:

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