Conjugate gradient methods and nonlinear optimization. (English) Zbl 0866.65037

Nocedal, Jorge

Adams, Loyce (ed.) et al., Linear and nonlinear conjugate gradient-related methods. Proceedings of the AMS-IMS-SIAM summer research conference, Washington, DC, USA, July 9–13, 1995. Philadelphia, PA: SIAM. 9-23 (1996).

Summary: This paper begins with a brief history of the conjugate gradient (CG) method in nonlinear optimization. A challenging problem arising in meteorology is then presented to illustrate the kinds of large-scale problems that need to be solved at present. The paper then discusses three current areas of research: the development and analysis of nonlinear CG methods, the use of the linear conjugate gradient method as an iterative linear solver in Newton-type methods, and the design of new algorithms for large-scale optimization that make use of the interplay between quasi-Newton and conjugate gradient methods.
For the entire collection see [Zbl 0857.00036].

MSC:

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

Keywords:

conjugate gradient method; nonlinear optimization; meteorology; large-scale problems; Newton-type methods; algorithms