TOMS765 or STENMIN
Large, sparse, unconstrained optimization using tensor methods.
Bouaricha, Ali (1997). STENMIN: A software package for large, sparse unconstrained optimization using tensor methods. ACM Transactions on Mathematical Software, 23(1), 81-90.
ABSTRACT OR SUMMARY
The STENMIN software package solves unconstrained optimization problems using an algorithm based on a tensor model, originally proposed by Schnabel and Chow, with order 1, that is, the model interpolates the last function value and gradient at each step. The package is designed for large problems whose Hessian matrices are sparse. The paper briefly describes the algorithm and gives results of tests comparing this package to MINPACK-2, a widely distributed optimization package for non-sparse problems, which is based on a non-tensor model. STENMIN is an outgrowth of an earlier package for nonlinear equations and least squares problems also based on tensor methods, which was described in a 1994 Argonne technical report by Bouaricha and Schnabel . That report, according to the bibliography of this paper, will appear in TOMS as an algorithm. [It has since appeared in the June 1997 issue.—ed.] One innovation in the STENMIN algorithm is the special treatment of the case where the Hessian has rank
n-1. The treatment is based on a method described by Bouaricha in another 1994 Argonne technical report . According to the reported test results, the new package is often more efficient than MINPACK-2 and considerably better on problems with a rank
n-1 Hessian. An interesting aspect of the package is the use of other publicly available software components: the Harwell Library MA27 package for sparse-matrix factorization and the Dennis and Schnabel line search. This gives more confidence that the test results are not artifacts of specialized matrix factoring or line search methods. Online Computing Reviews Service [ACM].
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