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The Computer Journal 1968 10(4):406-410; doi:10.1093/comjnl/10.4.406
© 1968 by British Computer Society
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Variance algorithm for minimization

W. C. Davidon *

Physics Institute, University of Arhus, Arhus, Denmark

An algorithm is presented for minimizing real valued differentiable functions on an N-dimensional manifold. In each iteration, the value of the function and its gradient are computed just once, and used to form new estimates for the location of the minimum and the variance matrix (i.e. the inverse of the matrix of second derivatives). A proof is given for convergence within N-iterations to the exact minimum and variance matrix for quadratic functions. Whether or not the function is quadratic, each iteration begins at the point where the function has the least of all past computed values.


* Physics Institute, University of Århus, Århus, Denmark. On leave from Haverford College, Haverford, Pa., 19041, U.S.A. This work was partly supported by a Fulbright–Hays grant.


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