The method of successive affine reduction for nonlinear minimization

Nazareth, J.L. (1986). The method of successive affine reduction for nonlinear minimization. Mathematical Programming 35 (1) 97-109. 10.1007/BF01589444.

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The traditional development of conjugate gradient (CG) methods emphasizes notions of conjugacy and the minimization of quadratic functions. The associated theory of conjugate direction methods, strictly a branch of numerical linear algebra, is both elegant and useful for obtaining insight into algorithms for nonlinear minimization. Nevertheless, it is preferable that favorable behavior on a quadratic be a consquence of a more general approach, one which fits in more naturally with Newton and variable metric methods. We give new CG algorithms along these lines and discuss some of their properties, along with some numerical supporting evidence.

Item Type: Article
Uncontrolled Keywords: conjugate gradients; high-dimensional optimization; Nonlinear minimization; successive affine reduction; variable storage algorithms
Depositing User: Luke Kirwan
Date Deposited: 09 Aug 2016 13:59
Last Modified: 27 Aug 2021 17:41

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