## 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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### References:

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