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Multiplier and gradient methods. (English) Zbl 0174.20705
Summary: The main purpose of this paper is to suggest a method for finding the minimum of a function \(f(x)\) subject to the constraint \(g(x)=0\). The method consists of replacing \(f\) by \(F=f+\lambda g+ \tfrac12 cg^2\), where \(c\) is a suitably large constant, and computing the appropriate value of the Lagrange multiplier. Only the simplest algorithm is presented.
The remaining part of the paper is devoted to a survey of known methods for finding unconstrained minima, with special emphasis on the various gradient techniques that are available. This includes Newton’s method and the method of conjugate gradients.

MSC:
65K10 Numerical optimization and variational techniques
49M15 Newton-type methods
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