Vol. 18, No. 1, 1966

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A convergent gradient procedure in prehilbert spaces

Edward Kenneth Blum

Vol. 18 (1966), No. 1, 25–30

In this paper, we present a new method of approximating the minimum of a functional, J, defined on a prehilbert space and subject to constraints of the form ψi(x) = 0, 1 i p, where the ψi are also functionals on the space. The method generates a convergent sequence of approximations using the gradients of J and ψi. However, it is not a steepest descent procedure with respect to J. A theorem is proven which establishes the convergence of the approximating sequence to the minimum.

Mathematical Subject Classification
Primary: 47.80
Received: 26 February 1965
Published: 1 July 1966
Edward Kenneth Blum