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

Authors:
Q. Ni and Y. Yuan

Journal:
Math. Comp. **66** (1997), 1509-1520

MSC (1991):
Primary 65K05, 90C06, 90C30

DOI:
https://doi.org/10.1090/S0025-5718-97-00866-1

MathSciNet review:
1422793

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we propose a subspace limited memory quasi-Newton method for solving large-scale optimization with simple bounds on the variables. The limited memory quasi-Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. The search direction consists of three parts: a subspace quasi-Newton direction, and two subspace gradient and modified gradient directions. Our algorithm can be applied to large-scale problems as there is no need to solve any subproblems. The global convergence of the method is proved and some numerical results are also given.

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Additional Information

**Q. Ni**

Affiliation:
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, P.O.Box 2719, Beijing 100080, China

Email:
niq@lsec.cc.ac.cn

**Y. Yuan**

Affiliation:
LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, P.O.Box 2719, Beijing 100080, China

Email:
yyx@lsec.cc.ac.cn

DOI:
https://doi.org/10.1090/S0025-5718-97-00866-1

Keywords:
Subspace quasi-Newton method,
limited memory,
projected search,
large-scale problem,
bound constrained optimization

Received by editor(s):
December 2, 1994

Received by editor(s) in revised form:
May 8, 1995, and January 26, 1996

Additional Notes:
The authors were partially supported by the Stat key project “Scientific and Engineering Computing” and Chinese NNSF grant 19525101.

Article copyright:
© Copyright 1997
American Mathematical Society