Unconstrained Optimization Packages

TENMIN Author Robert B. Schnabel
Department of Computer Science
University of Colorado
Boulder, CO 80309-0430
Phone: (303) 492-7554
E-mail: bobby@cs.colorado.edu
Language FORTRAN 77
Algorithm tensor method
Input Format  
Modeling Languages link  
Commercial Status free
Platform Any machine with a reasonable amount of memory and a Fortran compiler
Remarks TENMIN package is intended for solving unconstrained optimization problems where the number of variables n is not too large (n<100, say). The package allows the user to choose between a tensor method for unconstrained optimization and a standard method based on a quadratic model.
The tensor method bases each iteration upon a specially constructed fourth-order model of the objective function that is not significantly more expensive to form, store, or solve than the standard quadratic model. Both methods calculate the Hessian matrix and gradient vector, either analytically or by finite differences, at each iteration. The step selection strategy is a line search. The tensor method requires significantly fewer iterations and function evaluations to solve most unconstrained optimization problems than the standard method, and also solves a somewhat wider range of problems. It is especially useful for problems in which the Hessian matrix at the solution is singular.
References T. Chow, E. Eskow, and R. B. Schnabel, A software package for unconstrained optimization using tensor methods, Technical Report CU-CS-492-90, Department of Computer Science, University of Colorado, December 1990.
R. B. Schnabel and T. Chow, Tensor methods for unconstrained optimization using second derivatives, SIAM J. Optim. 1 (1991), pp. 293--315.