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283. MINIM: Function Minimization Package
by Nicholas E. Ertz, Department of Chemistry,
University of Iowa, Iowa City, Iowa 52240
This package consists of three subroutines and their
associated driver programs for finding the minimum of a
function f(X1,..., Xn). These subroutines are NEXTX,
LOWEST, and MINIMM.
Subroutine LOWEST: This subroutine performs algorithms
3 and 3a given by Murtagh and Sargent [Computer
Journal, 13, 185 (1970]. This is one of a class of
variable metric algorithms. It takes its first step as
the direction of steepest descent and then updates the
inverse of the Hessian matrix to determine successive
steps. Accurate line searches are not required, only
descent. If the method fails, the Hessian is thrown
out and the problem is restarted at the current point
with the unit matrix for the Hessian. If the stepsize
falls below a given level, the procedure stops (in
practice, this has yet to occur).
Subroutine NEXTX: This subroutine performs algorithms
3 and 3a given by Murtagh and Sargent [Computer
Journal, 13, 185 (1970]. This is one of a class of
variable metric algorithms. It takes its first step as
the direction of steepest descent and then updates the
inverse of the Hessian matrix to determine successive
steps. Accurate line searches are not required, only
descent. If the method fails, the Hessian is thrown
out and the problem is restarted at the current point
with the unit matrix for the Hessian. if the stepsize
falls below a given level, the procedure stops (in
practice, this has yet to occur).
The user has direct control over the function to be
minimized. This should allow for cleaner programming
and will facilitate overlay structure.
Subroutine MINIMM:This subroutine performs the
algorithm given by Jacobson and Oksman [J. Math. Anal.
and Appl., 38, 535 (1972)]. The method is exact for
homogeneous functions. Information about the Hessian
is not built up as in quadratic models. Instead, a
different set of basis vectors is used.
FORTRAN IV (IBM 360/370)
Lines of Code: 714
Recommended Citation: N. E. Ertz, QCPE 11, 283 (1975).
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