TENMIN

Unconstrained optimization

This package is intended for solving unconstrained optimization problems where the number of variables n is not too large (n less than 100, say), so that the cost of storing one n x n matrix and factoring it at each iteration is acceptable. 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.

The software can be called with an interface where the user supplies only the function, number of variables, and starting point; default choices are made for all other input parameters. An alternative interface allows the user to specify any input parameters that are different from the defaults.

The software is written in Fortran 77 using double precision. The only machine dependency is upon machine epsilon, which can be either calculated by the software or provided by the user.

Need more info?

Contact:

Robert B. Schnabel 
Department of Computer Science 
University of Colorado 
Boulder, CO 80309-0430
Phone: (303) 492-7554 
bobby@cs.colorado.edu

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.

[ Optimization Software Guide | OTC Home Page | NEOS Server | NEOS Guide ]