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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). |